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