Consider the following simple linear regression model: y = β0 + β1x + u. Using a sample of n observations on x and y, you estimate the model by OLS and obtain the estimates βˆ 0, βˆ 1, and the R-squared of the regression, R2 . Then you scale this sample by a factor of 100, obtain a new sample {xi/100; yi/100} for i = 1, . . . , n, re-estimate the model by OLS, and denote the new coefficient estimates by β˜ 0, β˜ 1, and the new R-squared of the regression by R˜2 . a) Give the expression of β˜ 1 in terms of βˆ 1, and justify your answer.

The accompanying table shows results from regressions performed on data from a random sample of 21 cars. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). Which regression equation is best for predicting city fuel consumption? Why? Click the icon to view the table of regression equations. Choose the correct answer below. A. The equation CITY=6.86 -0.00131WT -0.258DISP+0.659HWY is best because it has a low P-value and the highest value of R². B. The equation CITY=6.73 -0.00157WT +0.668HWY is best because it has a low P-value and the highest adjusted value of R². C. The equation CITY= -3.15+0.823HWY is best because it has a low P-value and its R² and adjusted R² values are comparable to the R² and adjusted R² values of equations with more predictor variables. O D. The equation CITY=6.86 -0.00131WT-0.258DISP + 0.659HWY is best because it…

The least-square regression line for the given data is y = 0.449x - 30.27. Determine the residual of a data point for which x = 90 and y=10, rounding to three decimal places. Temperature, x Number of absences, y OA. -0.14 OB. 20.14 C. 115.78 OD. 10.14 72 3 85 7 91 10 90 10 88 8 98 15 75 100 4 15 80- 5

A set of n = 25 pairs of scores (X and Y values) produces a regression equation Y = 3X – 2. Findthe predicted Y value for each of the following X scores: 0, 1, 3, -2.