SCMS 3711

True of False: The Chancellor of a university has commissioned a team to collect data on students' GPAs and the amount of time they spend bar hopping every week (measured in minutes). He wants to know if imposing much tougher regulations on all campus bars to make it more difficult for students to spend time in any campus bar will have a significant impact on general students' GPAs. His team should use a t test on the slope of the population regression.

true

True or False: A multiple regression is called "multiple" because it has several explanatory variables.

true

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

true

True or False: The coefficient of determination represents the ratio of SSR to SST.

true

True or False: When an additional explanatory or independent variable is introduced into a multiple regression model, the coefficient of multiple determination or R-square will never decrease.

true

The residual represents the discrepancy between the observed dependent variable and its _______ value.

predicted or estimated average

An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. SUMMARY OUTPUT Regression Statistics Multiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 ANOVA df SS MS F Signif F Regsion 2 33.4163 16.7082 186.325 0.0001 Resdual 7 0.6277 0.0897 Total 9 34.0440 Coeff StdError t Stat P-value Intcept - 0.0861 0.5674 - 0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price - 0.0006 0.0028 - 0.219 0.8330 Referring to Table 14-3, the p-value for the regression model as a whole is

0.0001

TABLE 13-5 The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyze the last 4 years of quarterly data (i.e., n = 16) with the following results: Regression Statistics Multiple R 0.802 R Square 0.643 Adjusted R Square 0.618 Standard Error SYX 0.9224 Observations 16 ANOVA df SS MS F Sig.F Regression 1 21.497 21.497 25.27 0.000 Error 14 11.912 0.851 Total 15 33.409 Predictor Coef StdError tStat P-value Intercept 3.962 1.440 2.75 0.016 Industry 0.040451 0.008048 5.03 0.000 Durbin-Watson Statistic 1.59 Referring to Table 13-5, the value of the quantity that the least squares regression line minimizes is ________. Hint: does the least squares line minimize the "good" or the "bad" variance?

11.912

TABLE 13-5 The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyze the last 4 years of quarterly data (i.e., n = 16) with the following results: Regression Statistics Multiple R 0.802 R Square 0.643 Adjusted R Square 0.618 Standard Error SYX 0.9224 Observations 16 ANOVA df SS MS F Sig.F Regression 1 21.497 21.497 25.27 0.000 Error 14 11.912 0.851 Total 15 33.409 Predictor Coef StdError tStat P-value Intercept 3.962 1.440 2.75 0.016 Industry 0.040451 0.008048 5.03 0.000 Durbin-Watson Statistic 1.59 Referring to Table 13-5, the estimates of the Y-intercept and slope are ________ and ________, respectively.

3.962 and .040451

TABLE 13-5 The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyze the last 4 years of quarterly data (i.e., n = 16) with the following results: Regression Statistics Multiple R 0.802 R Square 0.643 Adjusted R Square 0.618 Standard Error SYX 0.9224 Observations 16 ANOVA df SS MS F Sig.F Regression 1 21.497 21.497 25.27 0.000 Error 14 11.912 0.851 Total 15 33.409 Predictor Coef StdError tStat P-value Intercept 3.962 1.440 2.75 0.016 Industry 0.040451 0.008048 5.03 0.000 Durbin-Watson Statistic 1.59 Referring to Table 13-5, the prediction for a quarter in which X = 120 is Y = ________

8.816

The least squares method minimizes which of the following?

SSE (error)

The coefficient of multiple determination r2Y.12

measures the proportion of variation in Y that is explained by X1 and X2.

TABLE 14-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. SUMMARY OUTPUT Regression Statistics Multiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 ANOVA df SS MS F Signif F Regsion 2 33.4163 16.7082 186.325 0.0001 Resdual 7 0.6277 0.0897 Total 9 34.0440 Coeff StdError t Stat P-value Intcept - 0.0861 0.5674 - 0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price - 0.0006 0.0028 - 0.219 0.8330 Referring to Table 14-3, what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?

$2.89 billion

An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. SUMMARY OUTPUT Regression Statistics Multiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 ANOVA df SS MS F Signif F Regsion 2 33.4163 16.7082 186.325 0.0001 Resdual 7 0.6277 0.0897 Total 9 34.0440 Coeff StdError t Stat P-value Intcept - 0.0861 0.5674 - 0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price - 0.0006 0.0028 - 0.219 0.8330 Referring to Table 14-3, when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable, he obtained an r2 value of 0.971. What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression? In other words, the economist was explaining 97.1%, how much has that percentage or R-square increased after adding "price" as a second independent variable?

.011 or 1.1%

TABLE 14-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. SUMMARY OUTPUT Regression Statistics Multiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 ANOVA df SS MS F Signif F Regsion 2 33.4163 16.7082 186.325 0.0001 Resdual 7 0.6277 0.0897 Total 9 34.0440 Coeff StdError t Stat P-value Intcept - 0.0861 0.5674 - 0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price - 0.0006 0.0028 - 0.219 0.8330 1. Referring to Table 14-3, the p-value for GDP is

0.0001

TABLE 13-5 The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyze the last 4 years of quarterly data (i.e., n = 16) with the following results: Regression Statistics Multiple R 0.802 R Square 0.643 Adjusted R Square 0.618 Standard Error SYX 0.9224 Observations 16 ANOVA df SS MS F Sig.F Regression 1 21.497 21.497 25.27 0.000 Error 14 11.912 0.851 Total 15 33.409 Predictor Coef StdError tStat P-value Intercept 3.962 1.440 2.75 0.016 Industry 0.040451 0.008048 5.03 0.000 Durbin-Watson Statistic 1.59 Referring to Table 13-5, the coefficient of determination is ________.

0.643

TABLE 13-5 The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyze the last 4 years of quarterly data (i.e., n = 16) with the following results: Regression Statistics Multiple R 0.802 R Square 0.643 Adjusted R Square 0.618 Standard Error SYX 0.9224 Observations 16 ANOVA df SS MS F Sig.F Regression 1 21.497 21.497 25.27 0.000 Error 14 11.912 0.851 Total 15 33.409 Predictor Coef StdError tStat P-value Intercept 3.962 1.440 2.75 0.016 Industry 0.040451 0.008048 5.03 0.000 Durbin-Watson Statistic 1.59 Referring to Table 13-5, the correlation coefficient is ________.

0.802

TABLE 13-5 The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyze the last 4 years of quarterly data (i.e., n = 16) with the following results: Regression Statistics Multiple R 0.802 R Square 0.643 Adjusted R Square 0.618 Standard Error SYX 0.9224 Observations 16 ANOVA df SS MS F Sig.F Regression 1 21.497 21.497 25.27 0.000 Error 14 11.912 0.851 Total 15 33.409 Predictor Coef StdError tStat P-value Intercept 3.962 1.440 2.75 0.016 Industry 0.040451 0.008048 5.03 0.000 Durbin-Watson Statistic 1.59 Referring to Table 13-5, the standard error of the estimate is ________.

0.9224

The Y-intercept (b0) represents the

predicted value of Y when X = 0

The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by

error sum of squares.

If the Durbin-Watson statistic has a value close to 0, which assumption is violated? In other words, which assumption is the Durbin-Watson statistic checking to see is violated?

independence of errors

The slope (b1) represents

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

In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0, it means that

the estimated average of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constant.

The coefficient of determination (r2) tells us

the proportion of total variation that is explained

The standard error of the estimate is a measure of

the variation around the sample regression line