1 use the least square method to find regression

Question

The sales manager of a company would like to study the effect of the advertising on sales of GameToy. A sample of 22 cities with approximately equal popula­tion was selected for study during a test period of one month. Each city was allocated a specific expenditure level ($1000) and sales ($100000) during the test month were determined. The results are summarized below   

n=22     Σsales = 2695.3        Σsales² = 355288.93

Σadvertising = 550      Σadvertising² = 19250

Σadvertising.sales = 76672

Hint: First determine which variable is X and which is Y.

1) Use the least square method to find regression coefficients ß₀, and ß₁.

2) Interpret the meaning of regression coefficients in the context of this problem.

3) Predict the sales for the GameToy for a city in which $20000 has been spent for advertising.

4) Test whether the straight-line model contributes information for prediction of the dependent variable? Test using α=0.05. 

5) Compute the coefficient of determination and interpret its meaning in the context of the problem.

6) Compute the sample correlation coefficient and interpret its meaning in the context of the problem.

7) Compute the variance and define its meaning?