1. (Ten parts; 33 marks in total) Consider a SLR model to explore the association between selling price of a house (in thousands of dollars) and the square footage of the house. Use the SPSS output given below based on a random sample of 108 houses. Assume that all the assumptions are met for the required analysis. Use the following model for parts (a) - (j): u(price | saft) = Bo + Bi(saft) Descriptive Statistics Mean Std. Deviation N price 397.2869 104.59244 108 sqft 1760.0648 414.80024 108 ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 854698.400 000 Residual Total 1170535.000 a. Dependent Variable: Price b. Predictors: (Constant), sqftStat 252 Homework # 3 Questions Winter 2024 Coefficients' Unstandardized Standardized Coefficients Coefficients | B |StdEmor | Beta | Sig 1 {Constant) 18.056 22999 sqft 02154644 | 00127218 a. Dependent Variable: price a) (2 mark) According to the linear regression model, what is the predicted price of a house that is 2,000 square feet? b) (2 marks) What is the linear correlation coefficient for the relationship between price and square feet? c) (2 marks) What is the standard error of the model (standard deviation of the residuals)? d) (6 marks) Is there a linear relationship between average price and square footage? Carry out the most appropriate test using the t-distribution to answer this question. Use a significance level of 0.01. e) (4 marks) Calculate a 98% confidence interval for the slope of the regression line describing the relationship between square footage and mean selling price of a house. f) (5 marks) Calculate a 96% confidence interval for the average price of houses that are 1500 square feet. g) (3 marks) Calculate a 96% prediction interval for the selling price of a house that is 1500 square feet. h) (1 marks) How do your intervals in (f) and (g) compare? Which is wider? i) (6 marks) Is there a linear relationship between average price and square footage? Carry out the most appropriate test using the F-distribution to answer this question. Use a significance level of 0.01. i) (2 marks) Compare the test statistic and p-value from part (d) to the test statistic and p-value obtained in part (i). How are the test statistics related? How are the p-values related