FINAL EXAM STUDY GUIDE

In multiple regression analysis, the correlation among the independent variables is termed _____.

homoscedasticity

Below is a partial Excel output based on a sample of 25 observations. Coefficients Standard Error Intercept 145.321 48.682 x1 25.625 9.150 x2 −5.720 3.575 x3 0.823 0.183 The interpretation of the coefficient on x1 is that

idk

In a regression model involving 30 observations, the following estimated regression equation was obtained: ŷ = 17 + 4x1 − 3x2 + 8x3 + 8x4 For this model, SSR = 700 and SSE = 100. The computed F statistic for testing the significance of the above model is _____.

idk

In a simple regression analysis (where y is a dependent and x an independent variable), if the y-intercept is positive, then it must be true that _____.

idk

A multiple regression model has the form ŷ = 7 + 2 x1 + 9 x2 As x1 increases by 1 unit (holding x2 constant), ŷ is expected to _____.

increase by 2 units

If the coefficient of determination is equal to 1, then the coefficient of correlation _____.

can be either -1 or 1

If two variables, x and y, have a strong linear relationship, then _____.

x causes y to happen

A procedure used for finding the equation of a straight line that provides the best approximation for the relationship between the independent and dependent variables is ______.

least squares method

A regression analysis between sales (in $1000s) and price (in dollars) resulted in the following equation: ŷ = 50,000 − 8x The above equation implies that an increase of _____.

$1 in price is associated with a decrease of $8,000 in sales

Below you are given a partial Excel output based on a sample of 16 observations. ANOVA df SS MS F Regression 4,853 2,426.5 Residual 485.3 Coefficients Standard Error Intercept 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 We want to test whether the parameter β1 is significant. The test statistic equals _____.

-1.4 -3.682 / 2.630 = -1.4

The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). ŷ = 30 + 0.7x1 + 3x2 Also provided are SST = 1200 and SSE = 384. The multiple coefficient of determination is _____.

.32 1200 / 384

In a regression analysis, if SSE = 200 and SSR = 300, then the coefficient of determination is _____.

.600 300/500=.600 (SSE/SSE+SSR)

In a regression model involving 44 observations, the following estimated regression equation was obtained: ŷ = 29 + 18x1 + 43x2 + 87x3 For this model, SSR = 600 and SSE = 400. The coefficient of determination for the above model is _____.

.600 600 / 600+400 = .600

A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares: SSR = 165 SSE = 60 The coefficient of determination is _____.

.7333 165 / 225 = .7333

To test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.

14 and 240 14 255-1 = 254 - 14 = 240

A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have _____.

181 200 - 18- 1 = 181

Below is a partial Excel output based on a sample of 25 observations. Coefficients Standard Error Intercept 145.321 48.682 x1 25.625 9.150 x2 −5.720 3.575 x3 0.823 0.183 We want to test whether the parameter β1 is significant. The test statistic equals _____.

2.8 25.625 / 9.150

A regression analysis involved 6 independent variables and 27 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have _____.

20 27 - 6 - 1 = 20

In a regression model involving 44 observations, the following estimated regression equation was obtained: ŷ = 29 + 18x1 + 43x2 + 87x3 For this model, SSR = 600 and SSE = 400. MSR for this model is _____.

200 SSR / k 600/3

To test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.

4 and 31 4 and 36 - 4 - 1 = 31

Regression analysis was applied between sales data (in $1000s) and advertising data (in $100s), and the following information was obtained. ŷ = 12 + 1.8x n = 17 SSR = 225 SSE = 75 Sb1 = 0.2683 Refer to Exhibit 14-3. The F statistic computed from the above data is _____.

45 SSR/P / SSE/n-p-1 225/1 / 75/17-1-1= 45

The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). ŷ = 30 + 0.7x1 + 3x2 Also provided are SST = 1200 and SSE = 384. The yearly income of a 24-year-old male individual is _____.

49,800 y = 30 + (.7 *24) + (3*1) = 49.8 49.8 * 1000 = 49,800

Regression analysis was applied between sales data (in $1000s) and advertising data (in $100s), and the following information was obtained. ŷ = 12 + 1.8x n = 17 SSR = 225 SSE = 75 Sb1 = 0.2683 Refer to Exhibit 14-3. The t statistic for testing the significance of the slope is _____.

6.709 t= b1-B1/sb1 1.8 - 0 / .2683 = .6709

A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation: ŷ = 9 − 3x The above equation implies that if the price is increased by $1, the demand is expected to _____.

6000 units y= 9-3($1)=6 6*1000 units=6000

Regression analysis was applied between sales (in $1000s) and advertising (in $100s), and the following regression function was obtained. ŷ = 80 + 6.2x Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is _____.

62,080 80+6.2(10,000)

If the coefficient of correlation is .8, then the percentage of variation in the dependent variable explained by the estimated regression equation is _____.

64% .8^2=.64 .... 64%

Regression analysis was applied between sales data (in $1000s) and advertising data (in $100s), and the following information was obtained. ŷ = 12 + 1.8x n = 17 SSR = 225 SSE = 75 Sb1 = 0.2683 Refer to Exhibit 14-3. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is _____.

66,000 Given : x= 3,000 so 3,000/100= 30 times y= 12 + 1.8(30) = 66 times * ($1,000)

Below you are given a partial Excel output based on a sample of 16 observations. ANOVA df SS MS F Regression 4,853 2,426.5 Residual 485.3 Coefficients Standard Error Intercept 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 The sum of squares due to error (SSE) equals _____.

????

The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). ŷ = 30 + 0.7x1 + 3x2 Also provided are SST = 1200 and SSE = 384. If we want to test for the significance of the model, the critical value of F at a 5% significance level is _____.

??????

Below you are given a partial Excel output based on a sample of 16 observations. ANOVA df SS MS F Regression 4,853 2,426.5 Residual 485.3 Coefficients Standard Error Intercept 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals _____.

???????

The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). ŷ = 30 + 0.7x1 + 3x2 Also provided are SST = 1200 and SSE = 384. From the above function, it can be said that the expected yearly income for _____.

???????

The correct relationship between SST, SSR, and SSE is given by _____.

SSR = SST − SSE

Below is a partial Excel output based on a sample of 25 observations. Coefficients Standard Error Intercept 145.321 48.682 x1 25.625 9.150 x2 −5.720 3.575 x3 0.823 0.183 Carry out the test of significance for the parameter β1 at the 5% level. The null hypothesis should _____.

be rejected

In simple linear regression, r2 is the _____.

coefficient of determination

The interval estimate of the mean value of y for a given value of x is the _____.

confidence interval

A measure of the strength of the relationship between two variables is the _____.

correlation coefficient

If the coefficient of determination is a positive value, then the regression equation _____.

could have either a positive or a negative slope

If a qualitative variable has k levels, the number of dummy variables required is _____.

k-1

A regression model between sales (y in $1000s), unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function: ŷ = 7 − 3x1 + 5x2 For this model, SSR = 3500, SSE = 1500, and the sample size is 18.

increased by $1 (holding advertising constant), sales are expected to decrease by $3000

In a multiple regression model, the values of the error term, ε, are assumed to be _____.

independent of each other

A multiple regression model has _____.

more than one independent variable

If the coefficient of correlation is a negative value, then the coefficient of determination _____.

must be positive

Below you are given a partial Excel output based on a sample of 16 observations. ANOVA df SS MS F Regression 4,853 2,426.5 Residual 485.3 Coefficients Standard Error Intercept 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 Carry out the test of significance for the parameter β1 at the 1% level. The null hypothesis should _____.

not be rejected (?)

In a multiple regression analysis, SSR = 1,000 and SSE = 200. The F statistic for this model is _____.

not enough info (?)

Regression analysis is a statistical procedure for developing a mathematical equation that describes how _____.

one dependent and one or more independent variables are related

A data point (observation) that does not fit the trend shown by the remaining data is called a(n) _____.

outlier

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the _____.

residual

The primary tool or measure for determining whether the assumed regression model is appropriate is _____.

residual analysis

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called _____.

the regression model

In a multiple regression model, the variance of the error term ε is assumed to be _____.

the same for all values of the independent variable

As the goodness of fit for the estimated multiple regression equation increases, _____.

the value of the multiple coefficient of determination increases