Analytical Exercises:1) Data was collected from a random sample of 220 home sales from a community in 2003. Let𝑃 denote the selling price (in $1000), 𝐵𝑑𝑟 denote the number of bedrooms, 𝐵𝑎𝑡ℎ denote thenumber of bathrooms, 𝐻𝑆𝑖𝑧𝑒 denote the size of the house (in square feet), 𝐿𝑆𝑖𝑧𝑒 denote the lotsize (in square feet), 𝐴𝑔𝑒 denote the age of the house (in years), and 𝑃oor denote a variable thatis equal to 1 if the condition of the house is reported as “poor” and is zero otherwise. Anestimated regression yields the following fitted regression line:𝑃̂𝑖 = 119.2 + 0.485𝐵𝑑𝑟𝑖 + 23.4𝐵𝑎𝑡ℎ𝑖 + 0.156𝐻𝑆𝑖𝑧𝑒𝑖+ 0.002𝐿𝑆𝑖𝑧𝑒𝑖 + 0.090𝐴𝑔𝑒𝑖 − 48.8𝑃𝑜𝑜𝑟𝑖a) Interpret all the slope parameter estimates.b) Suppose that a homeowner converts part of an existing family room in her house intoa new bathroom. What is the regression’s prediction for the increase in the value of thehouse?c) Suppose that a homeowner adds a new bathroom to her house, which increases thesize of the house by 100 square feet. What is the regression’s prediction for the increasein the value of house? (Note that there are two things that change here)2) Suppose you’ve been asked by the Kansas City Royals baseball team to evaluate the economicimpact of their new stadium by analyzing the team’s attendance per game in the last year at theirold stadium. After some research on the topic, you decide on the following multiple linearregression model:𝐴𝑡𝑡𝑖 = 𝛽1 + 𝛽2𝑊𝑖𝑛𝑖 + 𝛽3𝑆𝑡𝑎𝑟𝑠𝑖 + 𝛽4𝑇𝑒𝑚𝑝𝑖 + 𝑢𝑖,Where:𝐴𝑡𝑡𝑖 = the attendance at the ith game.𝑊𝑖𝑛𝑖 = the winning percentage of the opponent in the ith game.𝑆𝑡𝑎𝑟𝑠𝑖 = the number of star players on the opposing team in the ith game.𝑇𝑒𝑚𝑝𝑖 = the outdoor temperature at the start of the ith game.You collect data on 40 games for all of the above variables and estimate the model via OLS. Youobtain the following estimates and associated standard errors:Parameter Estimate Standard Error𝛽2 15,000 10,0002𝛽3 2,000 3,000𝛽4 500 250a) Suppose you want to test the null hypothesis that the variable 𝑊𝑖𝑛𝑖 has no effect ongame attendance. Motivate and conduct a one-sided hypothesis test of this null hypothesis(that is, argue why you would use a one-sided test, then do it). Use the 5% significancelevel.b) Suppose you want to test the null hypothesis that the variable Stars has no effect ongame attendance. Motivate and conduct a one-sided hypothesis test of this null hypothesis.Use the 1% significance level.c) You’ve included the Temp variable because your boss thinks it’s important, but you’renot sure what you expect about this variable. Test the null hypothesis that Temp has noeffect on attendance using a two-sided hypothesis test. Use the 5% significance level.d) Construct a 95% confidence interval for the slope parameter on Temp, 𝛽43) Consider the following multiple linear regression model:𝑌𝑖 = 𝛽1 + 𝛽2𝑋2𝑖 + 𝛽3𝑋3𝑖 + 𝛽4𝑋4𝑖 + 𝛽5𝑋5𝑖 + 𝑢𝑖(Equation 1)You want to test the null hypothesis that neither 𝑋4𝑖 or 𝑋5𝑖 has an effect on 𝑌𝑖. You have a samplesize of 𝑛 = 55. Based on the following information:𝑌𝑖 = 𝛽1 + 𝛽2𝑋2𝑖 + 𝛽3𝑋3𝑖 + 𝑢𝑖(Equation 2)RSS for model in Equation 1: 100RSS for model in Equation 2: 120Conduct the test at both the 5% and 1% significance levels.4) Consider the following property of 𝑅2: it will not decrease if additional independent variablesare added into the regression model. If the independent variables are relevant in explaining thedependent variable, 𝑅2 will increase, if the independent variables are useless in explaining thedependent variable, 𝑅2 will stay the same. Use this property of 𝑅2to show that it is impossible toget a negative 𝐹 statistics in an 𝐹 test.