Please solve the following questions

a. Explain the logic of simple regression model diagrammatically. In what sense it is the best linear fit? b. A regression model was developed to find the determinants of home prices in a small city in Oklahoma. Data was collected from a number of cities on average market price of houses, average house size ( number of rooms in the house), average household income in dollar, Property tax rate, and percentage of commercial development. Output of the regression analysis is given below. House prices are in units of $ 1000. What is Predictor coef SE coef T P Constant -28.075 9.766 0.005 Home size 7.878 4.35 0.000 Household Income 0.00366 0.001344 2.73 0.008 Taxrate 43.09 -3.99 0.000 Commercial dev - 10.614 6.491 -1.64 Se = 3.67686 R2 = 47.4% R (adj) = 45% Analysis of Variance Source DF SS MS F P Regression 4 1037.49 259.37 19.19 0.000 Residualerror 85 1149.14 13.52 Total 89 2186.63 b.1. Write the population regression model and the estimated regression model. b.2. What is the standard error of the coefficient for home prices? b.3. Does a city's tax rate reduce the home price significantly. b.4. What is the expected price of a 3-bedroom house in a city with average household income of $35,000, a tax rate of 6%, and an overall 3% commercial development? b.5. Calculatea 95% confidence interval for the tax rate coefficient. b.6. What percent of the total variation in home prices is explained by the regression model? What are the drawbacks of R that led to the development of adjusted R