Overview
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Multiple linear regression analysis is an extension of our understanding of simple linear regression. The analysis involves the prediction of an outcome variable for two or more predictor variables. The calculations for finding the statistics are quite involved, so we’d want to appreciate the support of statistical software packages like R.
1) Using the Students_Performance data we've been working with, let’s begin to develop some sense-making around multiple linear regression analysis. Suppose we wanted to look at the relationship between two predictor variables (reading and writing scores) and one response variable (math scores).
a) Using the R codes for Assignment 8 provided in the Canvas Files folder, run a multiple linear regression to identify the regression coefficients, intercept and gradients, (in this context we call them partial gradients) for the independent variables.
b) Write the predictor equation.
c) Interpret the equation. Note: in the equation [Image unavailable: image.png], we'd say for each unit increase in x (predictor variable), there is a corresponding b1 unit change in y (response variable). In multiple linear regression, there is a b1 increase in y for each unit increase in X1 while holding the other variables constant; a b2 increase in y for each unit increase in X2 holding all other variables constant; etc.
2) Amend the R codes in Question 1 to perform a multiple linear regression analysis for the TV_Radio_Newspaper_Ads_Sales data in the Files folder in Canvas
a) Identify the regression coefficients
b) Write the predictor equation
c) Interpret the equation.
3) Amend the R codes again to perform a multiple linear regression analysis for the Condominiums_Price data in the Files folder in Canvas
a) Identify the regression coefficients
b) Write the predictor equation
c) Interpret the equation.