{"id":7648,"date":"2025-08-05T11:10:58","date_gmt":"2025-08-05T07:10:58","guid":{"rendered":"https:\/\/www.matsh.co\/en\/?p=7648"},"modified":"2025-08-05T11:10:58","modified_gmt":"2025-08-05T07:10:58","slug":"the-basics-of-regression-analysis-for-beginners","status":"publish","type":"post","link":"https:\/\/matsh.co\/en\/the-basics-of-regression-analysis-for-beginners\/","title":{"rendered":"The basics of regression analysis for beginners"},"content":{"rendered":"<p>Ever wondered how businesses predict sales trends or how researchers measure health outcomes? Many rely on <strong>regression<\/strong> techniques to uncover hidden patterns. This statistical approach helps identify connections between different <em>variables<\/em>, letting us model how changes in one factor might affect another.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/storage.googleapis.com\/48877118-7272-4a4d-b302-0465d8aa4548\/d8a69ed5-48d4-411f-8a77-974817c8fa5a\/f7cf7be9-472a-4180-b81a-576854c1f4cb.jpg\" alt=\"The basics of regression analysis for beginners\" \/><\/p>\n<p>At its core, <a href=\"https:\/\/www.qualtrics.com\/experience-management\/research\/regression-analysis\/\" target=\"_blank\" rel=\"noopener\">regression analysis<\/a> works by fitting lines or curves to <em>data<\/em> points. Simple models examine one influencing factor, like how study hours affect test scores. More complex versions account for multiple factors simultaneously\u2014think predicting house prices using square footage, location, and age.<\/p>\n<p>Why does this matter? From optimizing marketing budgets to improving patient care, these methods turn raw numbers into actionable insights. Unlike basic <em>correlation<\/em> (which only shows associations), regression reveals direction and magnitude\u2014helping us answer &#8220;how much&#8221; and &#8220;in what way.&#8221;<\/p>\n<h3>Key Takeaways<\/h3>\n<ul>\n<li>Identifies measurable connections between different factors in datasets<\/li>\n<li>Distinguishes between simple (one variable) and multiple (several variables) approaches<\/li>\n<li>Enables prediction of outcomes based on existing patterns<\/li>\n<li>Provides clearer insights than basic correlation measurements<\/li>\n<li>Essential tool for data-driven decision-making across industries<\/li>\n<\/ul>\n<p>Whether you&#8217;re analyzing customer behavior or climate trends, mastering these concepts unlocks deeper understanding. We&#8217;ll walk through practical examples showing how to apply these techniques effectively in real-world scenarios.<\/p>\n<h2>Introduction to Regression Analysis<\/h2>\n<p>What if you could mathematically explain why some neighborhoods have higher graduation rates or why certain products outsell others? This is where <strong>regression analysis<\/strong> shines\u2014it transforms vague hunches into quantifiable evidence through equations that map how <em>variables<\/em> interact.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/storage.googleapis.com\/48877118-7272-4a4d-b302-0465d8aa4548\/d8a69ed5-48d4-411f-8a77-974817c8fa5a\/7c63c921-db83-4868-9965-921ad1664583.jpg\" alt=\"regression analysis applications\" \/><\/p>\n<h3>Core Mechanics of Regression<\/h3>\n<p>At its simplest, this technique builds <em>models<\/em> using historical data. Imagine plotting student attendance against test scores. The resulting line doesn\u2019t just show a <em>relationship<\/em>\u2014it calculates how much each extra school day impacts final grades. More advanced versions handle multiple factors simultaneously, like predicting hospital readmissions using age, treatment type, and pre-existing conditions.<\/p>\n<h3>Where Theory Meets Practice<\/h3>\n<p>Businesses rely on these methods daily. Retailers forecast holiday sales by analyzing advertising budgets and consumer sentiment indexes. Healthcare teams estimate recovery timelines based on medication dosages and patient demographics. Even city planners use <em>regression<\/em> to reduce traffic accidents by testing how speed limits and weather patterns influence collision rates.<\/p>\n<ul>\n<li>Creates equations that quantify cause-and-effect relationships<\/li>\n<li>Supports data-driven decisions in education, healthcare, and urban planning<\/li>\n<li>Answers &#8220;what-if&#8221; scenarios through <em>prediction<\/em> capabilities<\/li>\n<\/ul>\n<p>Three goals guide every <strong>regression model<\/strong>: uncovering hidden connections between factors, forecasting future outcomes, and validating assumptions about how systems operate. We\u2019ll see how these purposes play out in concrete examples next.<\/p>\n<h2>Defining Variables: Dependent and Independent<\/h2>\n<p>Why do some variables drive changes while others simply follow along? Every regression model revolves around this fundamental question. We&#8217;ll unpack how to identify what&#8217;s being influenced versus what&#8217;s doing the influencing\u2014the cornerstone of effective analysis.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/storage.googleapis.com\/48877118-7272-4a4d-b302-0465d8aa4548\/d8a69ed5-48d4-411f-8a77-974817c8fa5a\/2ca5129c-f207-44e7-b47b-61f5f680cf86.jpg\" alt=\"dependent and independent variables example\" \/><\/p>\n<h3>Understanding the Role of Each Variable<\/h3>\n<p><strong>Dependent variables<\/strong> represent outcomes we want to explain or predict. Think of them as the &#8220;effect&#8221; in cause-effect relationships. In medical research, cholesterol levels might be our dependent variable\u2014the measurement we&#8217;re trying to understand through factors like age and exercise habits.<\/p>\n<p><strong>Independent variables<\/strong> act as potential influencers. These explanatory factors help us model changes in our outcome measurement. A housing study might use square footage and school district quality to predict home prices, as detailed in <a href=\"https:\/\/opentextbc.ca\/introductorybusinessstatistics\/chapter\/regression-basics-2\/\" target=\"_blank\" rel=\"noopener\">regression basics<\/a>.<\/p>\n<h3>Examples from Medical and Housing Data<\/h3>\n<p>Let&#8217;s examine real-world scenarios. Medical researchers analyzing heart health might track:<\/p>\n<ul>\n<li>Dependent variable: Cholesterol levels<\/li>\n<li>Independent variables: Weekly exercise hours, sodium intake, genetic markers<\/li>\n<\/ul>\n<p>In housing markets, the same principle applies differently:<\/p>\n<ul>\n<li>Dependent variable: Apartment rental prices<\/li>\n<li>Independent variables: Walkability scores, proximity to transit, unit age<\/li>\n<\/ul>\n<p>Notice how <em>variables switch roles<\/em> across studies. A patient&#8217;s age could be independent in cholesterol research but dependent in lifespan analysis. Proper identification before modeling prevents flawed conclusions\u2014a critical step many newcomers overlook.<\/p>\n<h2>The basics of regression analysis for beginners<\/h2>\n<p>How do we turn scattered data points into clear predictions? Let&#8217;s start with the simplest form\u2014<strong>linear regression<\/strong>. This method finds the straight line that best represents how two <em>variables<\/em> move together. Imagine plotting house sizes against prices on a graph. Each dot shows one home&#8217;s data. Our job? Draw the line that gets closest to all these points.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/storage.googleapis.com\/48877118-7272-4a4d-b302-0465d8aa4548\/d8a69ed5-48d4-411f-8a77-974817c8fa5a\/926cfadc-817d-446c-80e8-676c372b92c1.jpg\" alt=\"linear regression model scatter plot\" \/><\/p>\n<p>We use the <strong>method of least squares<\/strong> to calculate this line. It measures vertical distances between data points and our proposed line, then squares these gaps to eliminate negatives. The best fit line has the smallest total squared distance. Think of it as balancing accuracy across all observations.<\/p>\n<p>Why focus on straight lines first? Three key reasons:<\/p>\n<ul>\n<li>They provide a clear foundation for understanding more complex <em>relationships<\/em><\/li>\n<li>Equations like <em>y = mx + b<\/em> make predictions easy to calculate<\/li>\n<li>Visual patterns in scatter plots often reveal linear trends<\/li>\n<\/ul>\n<p>Once we&#8217;ve built our <strong>model<\/strong>, we can plug in new <em>values<\/em>. Want to estimate a 1,200 sq.ft. home&#8217;s price? Insert the number into the equation. While real-world data might curve or twist, linear <strong>regression<\/strong> gives us a powerful starting point for spotting meaningful patterns.<\/p>\n<p>Remember: Every model begins with this basic principle\u2014finding connections that help explain what we see and predict what comes next.<\/p>\n<h2>Exploring Simple and Multiple Linear Regression<\/h2>\n<p>How do we move from basic relationships to complex predictions? Let&#8217;s compare two powerful tools: simple and multiple linear <strong>regression<\/strong>. These methods build on each other, helping us model real-world patterns with increasing accuracy.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/storage.googleapis.com\/48877118-7272-4a4d-b302-0465d8aa4548\/d8a69ed5-48d4-411f-8a77-974817c8fa5a\/6f577553-490b-483f-9ebe-97dae0d5c5af.jpg\" alt=\"simple vs multiple linear regression comparison\" \/><\/p>\n<h3>Simple Linear Regression Explained<\/h3>\n<p>Imagine predicting someone&#8217;s weight using only their height. This single-predictor approach defines <em>simple linear regression<\/em>. The equation <strong>y = b\u2080 + b\u2081x<\/strong> maps how one <em>independent variable<\/em> (height) affects our <em>dependent variable<\/em> (weight).<\/p>\n<p>Here&#8217;s how it works:<\/p>\n<ul>\n<li>Plots data points on a scatter graph<\/li>\n<li>Draws the best-fitting straight line<\/li>\n<li>Calculates slope (b\u2081) and intercept (b\u2080)<\/li>\n<\/ul>\n<h3>Multiple Regression: More Variables at Play<\/h3>\n<p>Now add gender and age to our weight prediction. <strong>Multiple regression<\/strong> handles several <em>variables<\/em> simultaneously. The equation expands to <strong>y = b\u2080 + b\u2081x\u2081 + b\u2082x\u2082 + b\u2083x\u2083<\/strong>, where each x represents a different factor.<\/p>\n<table>\n<tr>\n<th>Aspect<\/th>\n<th>Simple Model<\/th>\n<th>Multiple Model<\/th>\n<\/tr>\n<tr>\n<td>Variables<\/td>\n<td>1 predictor<\/td>\n<td>2+ predictors<\/td>\n<\/tr>\n<tr>\n<td>Equation<\/td>\n<td>y = b\u2080 + b\u2081x<\/td>\n<td>y = b\u2080 + b\u2081x\u2081 + b\u2082x\u2082&#8230;<\/td>\n<\/tr>\n<tr>\n<td>Use Case<\/td>\n<td>Basic relationships<\/td>\n<td>Complex interactions<\/td>\n<\/tr>\n<tr>\n<td>Example<\/td>\n<td>Height \u2192 Weight<\/td>\n<td>Height + Age \u2192 Weight<\/td>\n<\/tr>\n<\/table>\n<p>While adding predictors often improves accuracy, irrelevant <em>variables<\/em> create noise. A good <strong>model<\/strong> balances detail with clarity. Start simple, then test if extra factors truly enhance predictions.<\/p>\n<h2>Key Assumptions in Linear Regression<\/h2>\n<p>Before trusting those neat regression results, we need to verify our model plays by the rules. Like checking your car&#8217;s tire pressure before a road trip, validating assumptions ensures our conclusions don\u2019t veer off course.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/storage.googleapis.com\/48877118-7272-4a4d-b302-0465d8aa4548\/d8a69ed5-48d4-411f-8a77-974817c8fa5a\/751cc2ee-bd8c-4b16-b041-82852b6b71c8.jpg\" alt=\"linear regression assumptions checklist\" \/><\/p>\n<h3>Linearity, Homoscedasticity, and Normality<\/h3>\n<p>First up: <strong>linearity<\/strong>. This means our <em>variables<\/em> should form a roughly straight-line pattern when plotted. If your scatterplot looks like a toddler\u2019s crayon scribble, linear regression might not fit.<\/p>\n<p><strong>Homoscedasticity<\/strong> sounds complex, but it\u2019s just fancy talk for &#8220;consistent spread.&#8221; Residuals (errors) should stay equally scattered across all predictor values. Picture bread slices with even jam coverage\u2014no thick globs at one end.<\/p>\n<p>The <strong>normality<\/strong> assumption focuses on error distribution. While models can handle some skewness, extreme outliers or lopsided patterns distort statistical tests. Think of it like baking cookies\u2014most should cluster near the center, not pile up on one tray edge.<\/p>\n<table>\n<tr>\n<th>Assumption<\/th>\n<th>Quick Check<\/th>\n<\/tr>\n<tr>\n<td>Linearity<\/td>\n<td>Scatterplot trends<\/td>\n<\/tr>\n<tr>\n<td>Homoscedasticity<\/td>\n<td>Residual vs fitted plots<\/td>\n<\/tr>\n<tr>\n<td>Normality<\/td>\n<td>Q-Q plots<\/td>\n<\/tr>\n<tr>\n<td>Multicollinearity<\/td>\n<td>VIF scores<\/td>\n<\/tr>\n<\/table>\n<p>Watch for <strong>multicollinearity<\/strong> too\u2014when predictors are overly chummy. High correlations between <em>variables<\/em> muddle their individual impacts. Use variance inflation factors (VIF) to spot troublemakers.<\/p>\n<p>Here\u2019s how we verify these conditions:<\/p>\n<ul>\n<li>Plot residuals against predictions to check spread patterns<\/li>\n<li>Run Shapiro-Wilk tests for normality<\/li>\n<li>Calculate correlation matrices between predictors<\/li>\n<\/ul>\n<p>Skip these checks, and you risk building models that crumble with new <em>data<\/em>. Solid assumptions create reliable insights\u2014worth the extra effort every time.<\/p>\n<h2>Method of Least Squares and Deriving Regression Coefficients<\/h2>\n<p>Precision matters when modeling relationships between variables. The <strong>method of least squares<\/strong> gives us mathematical certainty in finding the optimal <em>straight line<\/em> through scattered data points. Think of it as a treasure map where X marks the spot with minimal prediction errors.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/storage.googleapis.com\/48877118-7272-4a4d-b302-0465d8aa4548\/d8a69ed5-48d4-411f-8a77-974817c8fa5a\/25def3d6-f3c7-4ae4-88cc-9f89192d0d2e.jpg\" alt=\"least squares method visualization\" \/><\/p>\n<h3>Minimizing Residuals and Error Terms<\/h3>\n<p><strong>Residuals<\/strong> measure how far our predictions stray from reality. Each vertical gap between data points and the regression line represents an <em>error<\/em> (\u03b5). We square these differences to eliminate negative values and emphasize larger discrepancies.<\/p>\n<p>Here&#8217;s why squaring works better than absolute values:<\/p>\n<ul>\n<li>Penalizes large errors more heavily<\/li>\n<li>Creates differentiable functions for optimization<\/li>\n<li>Simplifies calculus-based solutions<\/li>\n<\/ul>\n<p><strong>Ordinary least squares<\/strong> (OLS) calculates <em>regression coefficients<\/em> by minimizing total squared residuals. The formula <em>\u03a3(y\u1d62 &#8211; \u0177\u1d62)\u00b2<\/em> becomes our compass, guiding us to the line where errors collectively shrink to their smallest possible sum.<\/p>\n<table>\n<tr>\n<th>Coefficient Sign<\/th>\n<th>Relationship<\/th>\n<th>Real-World Example<\/th>\n<\/tr>\n<tr>\n<td>b &gt; 0<\/td>\n<td>Positive<\/td>\n<td>More study hours \u2192 Higher test scores<\/td>\n<\/tr>\n<tr>\n<td>b <\/td>\n<td>Negative<\/td>\n<td>Higher interest rates \u2192 Lower home sales<\/td>\n<\/tr>\n<tr>\n<td>b = 0<\/td>\n<td>No correlation<\/td>\n<td>Shoe size vs. IQ scores<\/td>\n<\/tr>\n<\/table>\n<p>Interpreting these <em>coefficients<\/em> transforms raw numbers into stories. A positive <strong>b-value<\/strong> in <a href=\"https:\/\/www.sfu.ca\/~dsignori\/buec333\/lecture%208.pdf\" target=\"_blank\" rel=\"noopener\">regression basics<\/a> might reveal how each additional training hour boosts productivity. Negative values often signal trade-offs, like reduced customer satisfaction with faster delivery times.<\/p>\n<p>Through OLS, we transform chaotic data into clear directional insights. The math ensures our line isn&#8217;t just a guess\u2014it&#8217;s the statistically optimal path through uncertainty.<\/p>\n<h2>Interpreting Regression Outputs and Significance Tests<\/h2>\n<p>How do we separate meaningful patterns from random noise in data? Let\u2019s break down three critical elements in regression results: p-values, t-scores, and R\u00b2. These metrics help us distinguish real relationships from chance occurrences.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/storage.googleapis.com\/48877118-7272-4a4d-b302-0465d8aa4548\/d8a69ed5-48d4-411f-8a77-974817c8fa5a\/61b2ea6d-30ad-4692-99ed-d6cf21b55847.jpg\" alt=\"regression output interpretation\" \/><\/p>\n<h3>Understanding p-values and t-scores<\/h3>\n<p>A p-value acts like a truth detector. When it\u2019s below 0.05, we reject the <strong>null hypothesis<\/strong>\u2014the assumption that no relationship exists. Imagine testing if caffeine affects productivity. A p-value of 0.03 means there\u2019s only a 3% chance we\u2019d see this result if caffeine had zero real impact.<\/p>\n<p>T-scores measure how far our <em>regression coefficients<\/em> stray from zero, relative to data variation. Higher absolute values (usually above 2) suggest stronger evidence against the <strong>null hypothesis<\/strong>. Think of it as a signal-to-noise ratio for each predictor.<\/p>\n<h3>Coefficient of Determination (R\u00b2) Explained<\/h3>\n<p>R\u00b2 answers a simple question: What percentage of changes in our outcome can our model explain? A score of 0.75 means 75% of variance makes sense through our predictors. But context matters\u2014an R\u00b2 of 0.4 might be stellar in social sciences but weak in physics.<\/p>\n<p>When <a href=\"https:\/\/www.jmp.com\/en\/statistics-knowledge-portal\/what-is-regression\/interpreting-regression-results\" target=\"_blank\" rel=\"noopener\">interpreting regression outputs<\/a>, remember:<\/p>\n<ul>\n<li>Significant <em>coefficients<\/em> don\u2019t guarantee causation<\/li>\n<li>High R\u00b2 values can mask overfitting<\/li>\n<li>Always pair statistical <strong>tests<\/strong> with real-world logic<\/li>\n<\/ul>\n<p>We test if \u03b2 (the population slope) equals zero using these tools. If results show <strong>statistically significant<\/strong> relationships, we gain confidence to act on insights\u2014whether optimizing ad spend or improving patient treatments.<\/p>\n<h2>Real-World Applications of Regression Analysis<\/h2>\n<p>From farm fields to financial markets, regression techniques shape decisions that impact millions. These methods turn raw numbers into actionable strategies across industries, proving their versatility beyond textbooks.<\/p>\n<h3>Case Studies from Agriculture and Economics<\/h3>\n<p>Agricultural researchers rely on <strong>regression models<\/strong> to predict crop yields. By analyzing rainfall patterns, soil pH levels, and fertilizer use, farmers optimize planting schedules. A 2022 Midwest corn study found temperature explains 68% of yield variations\u2014critical knowledge for climate adaptation.<\/p>\n<p>Economists use similar methods to forecast unemployment trends. One Federal Reserve <em>model<\/em> combines consumer debt ratios, manufacturing output, and oil prices to predict recessions. During the 2020 pandemic, these <strong>predictions<\/strong> helped shape stimulus package allocations.<\/p>\n<p>Streaming platforms demonstrate marketing applications. By examining user <em>data<\/em> like age groups and watch times, services predict monthly streaming habits. A major platform improved content recommendations by 40% using viewing history <strong>analysis<\/strong>.<\/p>\n<table>\n<tr>\n<th>Industry<\/th>\n<th>Predictors<\/th>\n<th>Outcome<\/th>\n<\/tr>\n<tr>\n<td>Public Safety<\/td>\n<td>911 call frequency, response unit locations<\/td>\n<td>Optimal patrol routes<\/td>\n<\/tr>\n<tr>\n<td>Healthcare<\/td>\n<td>Medication dosage, patient age<\/td>\n<td>Recovery time estimates<\/td>\n<\/tr>\n<tr>\n<td>Retail<\/td>\n<td>Foot traffic, promo discounts<\/td>\n<td>Daily sales forecasts<\/td>\n<\/tr>\n<\/table>\n<p>Emergency services apply spatial <strong>regression<\/strong> to map 911 call hotspots. Cities like Chicago reduced average response times by 22% through geographic <em>data<\/em> analysis. Each <strong>example<\/strong> highlights how this tool adapts to diverse challenges, turning variables into solutions.<\/p>\n<h2>Advanced Techniques: Lasso, Ridge, and Spatial Regression<\/h2>\n<p>What happens when standard models struggle with too many features or geographic nuances? Modern regression techniques adapt to these challenges through smart mathematical adjustments. Let\u2019s explore methods that refine predictions while preventing common pitfalls.<\/p>\n<h3>Choosing the Right Penalty Approach<\/h3>\n<p><strong>Lasso regression<\/strong> (L\u2081 penalty) acts like a strict editor. It shrinks less important coefficients to zero, automatically selecting key predictors. Use this when facing data with hundreds of variables\u2014like gene expression studies\u2014to isolate truly impactful factors.<\/p>\n<p><strong>Ridge regression<\/strong> (L\u2082 penalty) takes a gentler approach. It reduces all coefficients without eliminating any, ideal for datasets with correlated predictors. This method stabilizes models when variables like income and education level move together.<\/p>\n<p>For location-based problems, <strong>geographically weighted regression<\/strong> shines. It recognizes that relationships between variables might change across regions. Analyzing housing markets? This technique could reveal how square footage impacts prices differently in coastal versus rural areas.<\/p>\n<p>These advanced models solve specific issues:<\/p>\n<ul>\n<li>Overcrowded datasets (Lasso)<\/li>\n<li>Multicollinearity (Ridge)<\/li>\n<li>Spatial variability (GWR)<\/li>\n<\/ul>\n<p>By matching the technique to the problem, we build models that balance accuracy with real-world practicality. Whether trimming unnecessary variables or accounting for geography, these tools expand what regression can achieve.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ever wondered how businesses predict sales trends or how researchers measure health outcomes? Many rely on regression techniques to uncover hidden patterns. This statistical approach helps identify connections between different variables, letting us model how changes in one factor might affect another. At its core, regression analysis works by fitting lines or curves to data [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[265],"tags":[],"class_list":["post-7648","post","type-post","status-publish","format-standard","hentry","category-education"],"acf":[],"_links":{"self":[{"href":"https:\/\/matsh.co\/en\/wp-json\/wp\/v2\/posts\/7648","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/matsh.co\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/matsh.co\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/matsh.co\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/matsh.co\/en\/wp-json\/wp\/v2\/comments?post=7648"}],"version-history":[{"count":1,"href":"https:\/\/matsh.co\/en\/wp-json\/wp\/v2\/posts\/7648\/revisions"}],"predecessor-version":[{"id":7698,"href":"https:\/\/matsh.co\/en\/wp-json\/wp\/v2\/posts\/7648\/revisions\/7698"}],"wp:attachment":[{"href":"https:\/\/matsh.co\/en\/wp-json\/wp\/v2\/media?parent=7648"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matsh.co\/en\/wp-json\/wp\/v2\/categories?post=7648"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matsh.co\/en\/wp-json\/wp\/v2\/tags?post=7648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}