Question

For chapter 1 problem 6 of the Applied Linear Regression Models 4th Edition book, I found the formula using B_0 (200) and B_1 (5), my equation is y=200+5x. How do you calculate the error terms e_i or graph the error terms with the correlating data points when the only other information given is just the standard deviation equals 4?

Answer 1

Answer

The linear model is: y_i = β₀ + β₁x_i + e_i, where e_i is the error term.

The regression equation is given by: y_icap = β_0cap + β_1capx_i, where β_0cap + β_1cap are the least square estimates of β₀ and β₁

Thus, the error term, e_i = y_i - y_icap

So, to obtain the error terms, e_i from the given data points, substitute each x_i value in the regression equation to get y_icapand then subtract this estimated value from the corresponding y-value in the data point to get the error e_i. Repeat this for all i's. Plot these e_i’s against the x_i values to get the plot/graph of the residuals.      

DONE