Suppose you have been given a dataset containing information on the monthly sales (Y) and advertising expenditure (X) for a company over a period of 24 months. You are interested in estimating the relationship between sales and advertising and want to test whether advertising has a significant effect on sales.

(a) Write down the simple linear regression equation for this model.

(b) Calculate the sample mean and sample standard deviation for both Y and X.

(c) Calculate the sample correlation coefficient between Y and X.

(d) Estimate the slope coefficient (?) and intercept (?) of the regression equation.

(e) Interpret the estimated intercept and slope coefficient in the context of the problem.

(f) Test the hypothesis that the slope coefficient is equal to zero against the alternative that it is not equal to zero at a 5% significance level. State the null and alternative hypothesis, calculate the test statistic, and draw a conclusion.

(g) Calculate the coefficient of determination (R-squared) for this regression model and interpret its meaning.