Week-3-codes

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5570

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Statistics

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Nov 24, 2024

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MGEC11 Week 3 Codes Yue Yu Fall 2023 library (wooldridge) Determinants of College GPA data ( gpa1 ) ols1 <- lm (colGPA ~ hsGPA + ACT, data = gpa1) summary (ols1) ## ## Call: ## lm(formula = colGPA ~ hsGPA + ACT, data = gpa1) ## ## Residuals: ## Min 1Q Median 3Q Max ## -0.85442 -0.24666 -0.02614 0.28127 0.85357 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 1.286328 0.340822 3.774 0.000238 *** ## hsGPA 0.453456 0.095813 4.733 5.42e-06 *** ## ACT 0.009426 0.010777 0.875 0.383297 ## --- ## Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 ## ## Residual standard error: 0.3403 on 138 degrees of freedom ## Multiple R-squared: 0.1764, Adjusted R-squared: 0.1645 ## F-statistic: 14.78 on 2 and 138 DF, p-value: 1.526e-06 Q1: What’s the impact of high school GPA on college GPA? Holding all the other factors constant, an increase in high school GPA by one point leads to an increase in college GPA by 0.45. Q2: Is 0.45 a dramatic increase? Compare the effect with the difference between 25 percentile and 75 percentile: summary (gpa1 $ colGPA) ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 2.200 2.800 3.000 3.057 3.300 4.000 College GPA at 75 percentile is 3.3 and college GPA at 25 percentile is 2.8. A 0.45 point increase in college GPA moves one from 25 percentile to (almost) 75 percentile. 1

Q3: What’s the impact of ACT on college GPA? Holding all the other factors constant, an increase in ACT by one point raises college GPA by only 0.01 point. Compared to 0.5 or 0.37, this is a relatively small effect. Q4: How much of the variation in college GPA can be explained by ACT and high school GPA? Joint together, these two factors can explain 17.6% of the total variation in college GPA. Q5: How to interpret the intercept? The intercept 1.29 is the predicted college GPA if high school GPA and ACT are both set at zero. Since no one who attends college has either a zero high school GPA or a zero on the ACT, the intercept in this equation is not very meaningful. 2

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