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Discuss and explain each of the assumptions of the simple linear regression model.
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- Imagine you are trying to explain the effect of square footage on home sale prices in the United States. You collect a random sample of 100,000 homes that recently sold. a) Homes can be one of three types: single-family houses, townhomes, or condos. How would you control for a home’s type in a regression model? b) Write down a regression model that includes controls for home type, square footage, and number of bedrooms. c) How would you interpret the es3mated coefficients for each of the variables from part b? Be specific.In multiple regressions, the correlation coefficient of each independent variable can be measured in addition to the multiple correlation coefficient. How do the values of individual correlation coefficients compare to the value of the multiple correlation coefficient?The table below shows the number, in thousands, of vehicles parked in the central business district of a certain city on a typical Friday as a function of the hour of the day. Hour of the day Vehicles parked(thousands) 9 A.M. 6.2 11 A.M. 7.4 1 P.M. 7.5 3 P.M. 6.6 5 P.M. 3.9 (a) Use regression to find a quadratic model for the data. (Let V be the number of vehicles and t be the time in hours since midnight. Round the regression parameters to three decimal places.) V = (b) Express using functional notation the number of vehicles parked on a typical Friday at 4 P.M., and then estimate that value. (Round your answer to two decimal places.) V = = thousand