2. Find the regression line for predicting overall university GPA from high scho
ID: 3232996 • Letter: 2
Question
2. Find the regression line for predicting overall university GPA from high school GPA, math SAT scores, verbal SAT scores.
below is a screenshot of the results I obtained.
a) Does the model do a good job of predicting university GPA? Explain and provide relevant statistics (e.g. significant test, R squared)
b) Which independent variables are good predictors if any? Explain and provide relevant statistics (e.g. significance test for each coefficient). For significant predictors, what is the direction of the relationship?
Call: lm formula d$univ GPA. d$high GPA d$math SAT d$verb SAT) Residuals: 1Q Median Min 3Q Max 0.68186 -0.13189 0.01289 0.16186 0.93994 Coefficients Estimate Std. Error t value Pr C> tl) CIntercept) 0.5793478 0.3422627 1.693 0.0936 d$high GPA 0.5454213 0.0850265 6.415 4.6e-09 d$math SAT 0.0004893 0.0010215 0.479 0.6330 d$verb SAT 0.0010202 0.0008123 1.256 0.2120 Signif. codes: 0 0.001 3 0.01 0.05 0.1 1 Residual standard error: 0.2784 on 101 degrees of freedom Multiple R-squared 0.6236, Adjusted R-squared 0.6124 F-statistic: 55.77 on 3 and 101 DF, p-value 2.2e-16Explanation / Answer
a)
F test statistics is
F = 55.77
The p-value is: 0.0000
Since p-value is less than 0.05 so model is significant to the model.
The r-square is: 0.6236
That is 62.36% of variation in dependent variable is explained by independent variable.
b)
The variable : high_GPA
The t -test statistics is
t = 6.415
The p-value is : 0.000
Since p-value is less than 0.05 so this variable is significant to the model.
The variable : math_SAT
The t -test statistics is
t = 0.479
The p-value is : 0.633
Since p-value is greater than 0.05 so this variable is not significant to the model.
The variable : math_verb
The t -test statistics is
t = 1.256
The p-value is : 0.2120
Since p-value is greater than 0.05 so this variable is not significant to the model.
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