BDA Chapter 12

Referring to Table 12-2, what is the standard error of the regression slope estimate, ? a) 12.650 b) 0.885 c) 16.299 d) 0.784

a) 12.650

Referring to Table 12-2, if the price of the candy bar is set at $2, the estimated mean sales will be a) 65. b) 100. c) 30. d) 90.

a) 65.

TABLE 12-1 A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y) - measured in dollars per month - for services rendered to local companies. One independent variable used to predict service charges to a company is the company's sales revenue (X) - measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model: Y1 - β0 + β1X1 + εi The results of the simple linear regression are provided below. Y = -2,700 + 20 X, SYX = 65, two-tail p-value = 0.034 (for testing β1) Referring to Table 12-1, interpret the estimate of σ, the standard deviation of the random error term (standard error of the estimate) in the model. a) About 95% of the observed service charges fall within $130 of the least squares line. b) About 95% of the observed service charges fall within $65 of the least squares line. c) For every $1 million increase in sales revenue, we expect a service charge to increase $65. d) About 95% of the observed service charges equal their corresponding predicted values.

a) About 95% of the observed service charges fall within $130 of the least squares line.

Regression analysis is used for prediction, while correlation analysis is used to measure the strength of the association between two numerical variables. a) True b) False

a) True

The Regression Sum of Squares (SSR) can never be greater than the Total Sum of Squares (SST). a) True b) False

a) True

Referring to Table 12-7, which of the following will be a correct conclusion? a) You can reject the null hypothesis and, therefore, conclude that there is sufficient evidence to show that the prison stocks portfolio and S&P 500 Index are negatively related. b) You can reject the null hypothesis and conclude that there is insufficient evidence to show that the prison stocks portfolio and S&P 500 Index are negatively related. c) You cannot reject the null hypothesis and, therefore, conclude that there is sufficient evidence to show that the prison stocks portfolio and S&P 500 Index are negatively related. d) You cannot reject the null hypothesis and, therefore, conclude that there is insufficient evidence to show that the prison stocks portfolio and S&P 500 Index are negatively related.

a) You can reject the null hypothesis and, therefore, conclude that there is sufficient evidence to show that the prison stocks portfolio and S&P 500 Index are negatively related.

The coefficient of determination (r2) tells you a) whether r has any significance. b) the proportion of total variation that is explained. c) that you should not partition the total variation. d) that the coefficient of correlation (r) is larger than 1.

a) whether r has any significance.

Referring to Table 12-2, what is the coefficient of correlation for these data? a) 0.7839 b) -0.7839 c) 0.8854 d) -0.8854

b) -0.7839

TABLE 12-2 A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below: City Price ($) Sales River Falls 1.30 100 Hudson 1.60 90 Ellsworth 1.80 90 Prescott 2.00 40 Rock Elm 2.40 38 Stillwater 2.90 32 Referring to Table 12-2, what is the estimated mean change in the sales of the candy bar if price goes up by $1.00? a) 0.784 b) -48.193 c) 161.386 d) -3.810

b) -48.193

TABLE 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows. Broker Clients Sales 1 27 52 2 11 37 3 42 64 4 33 55 5 15 29 6 15 34 7 25 58 8 36 59 9 28 44 10 30 48 11 17 31 12 22 38 Referring to Table 12-4, the least squares estimate of the Y-intercept is ________.

17.7

Referring to Table 12-4, the prediction for the amount of sales (in $1,000s) for a person who brings 25 new clients into the firm is ________.

45.66

TABLE 12-2 A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below: City Price ($) Sales River Falls 1.30 100 Hudson 1.60 90 Ellsworth 1.80 90 Prescott 2.00 40 Rock Elm 2.40 38 Stillwater 2.90 32 Referring to Table 12-2, what is the estimated slope for the candy bar price and sales data? a) 161.386 b) -48.193 c) -3.810 d) 0.784

b) -48.193

Referring to Table 12-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 Index, the p-value of the associated test statistic is ________. a) 2.94942E-07 b) 2.94942E-07 / 2 c) 8.7932E-13 d) (2.94942E-07)2

b) 2.94942E-07 / 2

The Durbin-Watson D statistic is used to check the assumption of normality. a) True b) False

b) False

The value of r is always positive. a) True b) False

b) False

TABLE 12-7 An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the market index like the S&P 500, then it is possible to reduce the variability of the portfolio's return. In other words, one can create a portfolio with positive returns but less exposure to risk. A sample of 26 years of S&P 500 Index and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 Index, is collected. A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y) on the returns of S&P 500 Index (X) to prove that the prison stocks portfolio is negatively related to the S&P 500 Index at a 5% level of significance. The results are given in the following Microsoft® Excel output. Note: 2.94942E-07 = 2.94942 * 10-7 Referring to Table 12-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 Index, the appropriate null and alternative hypotheses are, respectively, a) H0: r ≥ 0 vs. H1: r < 0. b) H0: ρ ≥ 0 vs. H1: ρ < 0. c) H0: r ≤ 0 vs. H1: r > 0. d) H0: ρ ≤ 0 vs. H1: ρ > 0.

b) H0: ρ ≥ 0 vs. H1: ρ < 0.

The slope (b1) represents a) the predicted value of Y. b) the estimated average change in Y per unit change in X. c) predicted value of Y when X = 0. d) variation around the line of regression.

b) the estimated average change in Y per unit change in X.

Referring to Table 12-2, what is the standard error of the estimate, SYX, for the data? a) 0.784 b) 0.885 c) 16.299 d) 12.650

c) 16.299

Referring to Table 12-2, what percentage of the total variation in candy bar sales is explained by the prices? a) 48.19% b) 100% c) 78.39% d) 88.54%

c) 78.39%

Based on the residual plot below, you will conclude that there might be a violation of which of the following assumptions? a) normality of errors b) linearity of the relationship c) homoscedasticity d) independence of errors

c) homoscedasticity

In performing a regression analysis involving two numerical variables, you are assuming a) that X and Y are independent. b) the variances of X and Y are equal. c) the variation around the line of regression is the same for each X value. d) all of the above

c) the variation around the line of regression is the same for each X value.

The standard error of the estimate is a measure of a) total variation of the Y variable. b) explained variation. c) the variation around the sample regression line. d) the variation of the X variable.

c) the variation around the sample regression line.

Referring to Table 12-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 Index, the measured value of the test statistic is ________. a) -0.503 b) 0.357 c) 0.072 d) -7.019

d) -7.019

The residuals represent a) the predicted value of Y for the average X value. b) the difference between the actual Y values and the mean of Y. c) the square root of the slope. d) the difference between the actual Y values and the predicted Y values.

d) the difference between the actual Y values and the predicted Y values.

Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals -0.30, a) the variance of X is negative. b) variable X is larger than variable Y. c) there is no correlation. d) the slope (b1) is negative.

d) the slope (b1) is negative.