If you can please show work. Thanks! 5. Suppose we fit a multiple linear regress
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If you can please show work. Thanks!
5. Suppose we fit a multiple linear regression GPA-? +ASAT +AAGE and obtain estimates ? 0.1, ?,-0.008, -0.1. (a) In words, interpret the meaning of = 0.008. (b) Suppose you previously fitted a simple linear regression GPA a + BSAT and found that the coefficient of determination R0.62, while the multiple linear regression with SAT and AGE as predictors gave you R0.77. Explain, how you would use this information to compare the two regression models (i.e. explain which model is better and why)Explanation / Answer
Answer (a)
The coefficient of SAT ?1 is 0.008. The value of coefficient indicates that keeping other variables constant, student with higher SAT score is expected to have higher GPA. For every one unit increase in SAT score, you can expect GPA to increase by an average of 0.008.
Answer (b)
Coefficient of determination is a measure of how much of the variability in one variable can be "explained by" variation in the other. Coefficient of determination R12 is 0.62 for simple linear regression GPA = ? + ?SAT. This means that 62% of the variability in GPA is explained by SAT score.
Coefficient of determination R12 is 0.62 for simple linear regression GPA = ? + ?1SAT + ?2AGE. This means that 77% of the variability in GPA is explained by SAT score and Age.
The higher R-squared values represent smaller differences between the observed data and the fitted values. In other words, the higher the value, the better the fit. The model 2 is better as coefficient of determination of model 2 (0.77) is higher than coefficient of determination of model 1 (0.62).
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