For certain data the following regression equations were obtained: 4x – 5y + 33 = 0 20x + 9y -- 107 = 0 Estimate y when x = 20 and x when y = 20 %3D %3D

Data from 147 colleges from 1995 to 2005 (Lee,2008) were tested to predict the endowments (in billions) to a college from the average SAT score of students attending the college. The resulting regression equation was Y = -20.46 + 4.06 (X). This regression indicates that: a. for every one-point increase in SAT scores, a college can expect 4.06 billion more in endowments. b. most colleges have very high endowments. c. for every one-point increase in SAT scores, a college can expect 20.46 billion fewer in endowments. d. for every one-dollar increase in endowments, the college can expect a half-point increase in SAT scores.

A researcher is interested in finding out the factors which determined the yearly spending on family outings last year ​(Y​, measured in​ dollars). She compiles data on the number of members in a family ​(X1​), the annual income of the family ​(X2​), and the number of times the family went out on an outing in the last year ​(X3​). She collects data from 196 families and estimates the following​ regression:   Y=120.45+1.54X1+2.12X2+2.12X3.   Suppose β1​, β2​, β3​, denote the population slope coefficients of X1​, X2​, and X3​, respectively.   The researcher wants to check if neither X1 nor X2 have a significant effect on Y or at least one of them has a significant​ effect, keeping X3 constant. She calculates the value of the F​-statistic for the test with the two restrictions ​(H0: β1=0, β2=0 vs. H1: β1≠0 and/or β2≠0​) to be 3.00.   The p​-value for the test will be enter your response here?

The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ý = 82.3 + 2.29x, + 1.90x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.415. (a) Compute and interpret R? and R 2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is 653 x . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R2 = 0.653 and R,2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis (is preferred since both R2 and R.2 show an increased v v…