MULTIPLE CHOICE (30 points: each question 3 points) Identify the letter of the choice that best completes the statement or answers the question. 1. Let for the random variable Y, we know that E(Y)=1,V(Y)=4. Also let Z=6Y-2. What is E(Z) and V(Z) ? 4 and 1 2 and 144 2 and 1 4 and 144 2. For 3 random variables X_1, X_2 and Y, Cov(X_1-X_2,Y) is equal to Cov(X_1,Y)-Cov(X_2,Y) Cov(X_1,Y)+Cov(X_2,Y) Cov(X_1,Y) Cov(X_2,Y) The regression line = 3 + 2x has been fitted to the data points (4, 8), (2, 5), and (1, 2). The sum of the squared residuals will be: 7 15 8 22 A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least squares line: (Sales) = 80,000+4 Advertising. This implies that: an increase of $1 in advertising is expected to result in an increase of $4 in sales an increase $4 in advertising is expected to result in an increase of $4,000 in sales an increase of $1 in advertising is expected to result in an increase of $80,004 in sales an increase of $1 in advertising is expected to result in an increase of $4,000 in sales Given the least squares regression line Y = 2.48 - 1.63 X, and a coefficient of determination of 0.81, the coefficient of correlation is: -0.85 0.85 -0.90 0.90 The state of Minnesota wants to know whether restricting the opening hours of liquor stores reduces alcohol consumption. You gather a data set that contains the following information: alcohol_i = per capital