Question 1. (a)

R²= 4.33% of the variation in the dependent variable RET is explained by the variation of the independent variables: GRI, SAT, TEN, Age, and MBA. We cannot assume from the low R squared that the model is useless because there might be one or more independent variables that are not significant to the dependent variable. Also, we cannot question the fact that the OLS are not accurate just by looking at the low R squared. In the opposite, adding new independent variables do increase the R squared even if they are not directly linked to the dependent variable, but do not make the regression useful. Besides, by using Excel, we can find out whether the model fits well data or not by referring to the F significance. We have HO: the model does not fit well the data and H1: the model does fit well the data. F significance is equal to 0.00024452 which is less than α. We then reject HO and conclude that the model fits well the data and is not useless.

Question 1. (b)
Let us suppose that we have sales as dependent variable. We want to regress sales against the following independent variables: price, gender, ads, population, inflation, service, GDP, location, types of products, preferences, season, awareness, suppliers, demanders, number of smokers, height, and weight. As long as we increase the number of the independent variables, the R² increases even though some independent variables are not significant to the dependent variable. Using the F-test that measures overall goodness of fit, we are likely to accept H0 while we should reject it.

Question 1. (c)

To check the linearity, we have to test whether an independent variable has a linear relationship with the dependent variable here the RET or not.
-For the GRI variable we have:
H0: GRI and RET have linear relationship
H1: GRI and RET do not have linear relationship
According the graph and