a. Fit a linear model where the square footage of the house is used to predict the sale price. (X=sqft and Y=price). Write the estimated regression equation. b. Interpret the estimate of the slope. c. Test whether square footage has a significant linear relationship with price. Use a = 0.05 level of significance. Write the null and alternative hypothesis, state the test statistic and p-value, and make a conclusion. d. Now test whether square footage has a significant positive linear relationship with price. Use a =0.05 level of significance. Write the null and alternative hypothesis, state the test statistic and p-value, and make a conclusion. e. Find and interpret a 95% confidence interval for the mean price when sqft=2000. f. Find and interpret a 95% prediction interval for the price when sqft-2000. g. What would happen to the interval from part f. if the confidence level is decreased to 90%? Explain in a sentence or two. h. Run a summary of your dataset (in R, this is: summary (dataset) ). Would it make sense to predict the sale price of a house that is 8500 square feet? i. What would happen to the interval from part f. if the confidence level is increased to 100%? Explain in a sentence or two