The CTO Corporation has a large number of chain restaurants throughout the United States. The research department at the company wanted to find if the restaurants’ sales depend on the mean income of households in the related areas. The company collected information on these two variables for 10 restaurants randomly selected from different areas. The following table gives information on the weekly sales (in thousands of dollars) of these restaurants and the mean annual incomes (in thousands of dollars) of the households for those areas.

a. Taking income as an independent variable and sales as a dependent variable, compute SSxx, SSyy, and SSxy.
b. Find the least squares regression line.
c. Briefly explain the meaning of the values of a and b calculated in part b.
d Calculate r and r2 and briefly explain what they mean.
e. Compute the standard deviation of errors.
f. Construct a 95% confidence interval for B.
g. Test at a 2.5% significance level whether B is positive.
h. Using a 2.5% significance level, test whether ρ is positive.

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Sales 26 38 23 30 22 40 44 32 28 47 55 Income 46 48 63 52 58 41 49 32 72