A multiple regression analysis between yearly income (Y in $1,000s), college grade point average (X1), age...
A multiple regression analysis between yearly income (Y in $1,000s), college grade point average (X1), age of the individuals (X2), and the gender of the individual (X3; zero representing female and one representing male) was performed on a sample of 10 people, and the following results were obtained.
Coefficient Standard Error
Constant 4.0928 1.4400
X1 10.0230 1.6512
X2 0.1020 0.1225
X3 -4.4811 1.4400
Analysis of Variance
Source DoF SoS MS F
Regression ? 360.59 ? ?
Error ? 23.91 ? ?
(a) Write the regression equation for the above.
(b) Interpret the meaning of the coefficient of X3.
(c) Compute the coefficient of determination.
(d) Is the coefficient of X1 significant? Use a = 0.05.
(e) Is the coefficient of X2 significant? Use a = 0.05.
(f) Is the coefficient of X3 significant? Use a= 0.05.
(g) Perform an F test and determine whether or not the model is significant.
Homework Answers
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A multiple regression analysis between yearly income (Y in
$1,000s), college grade point average (X1), age...
1. A multiple regression analysis between yearly income (Y in $1,000s), college grade point average (X1),...
1. A multiple regression analysis between yearly income (Y in $1,000s), college grade point average (X1), age of the individuals (X2), and the gender of the individual (X3; zero representing female and one representing male) was performed on a sample of ten students, and the following results were obtained: Coefficients Standard Error p-value Intercept 4.0928 1.4400 X1 10.0230 1.6512 X2 0.1020 0.1225 X3 ‐4.4811 1.4400 ANOVA DF SS MS Regression 360.59 Residual error 23.91 a. Write the regression...
11. (25 points) A multiple regression analysis is conducted to determine factors that relate to the...
11. (25 points) A multiple regression analysis is conducted to determine factors that relate to the success of sales associates. The regression is conducted between annual sales (Y in $1,000s), years of experience gion (X3; zero representing USA and 1 representing Canada) was performed on a sample of 29 people, and the following results were obtamed where SSR 84 60 amd SSE 57.5. Standard Coefficient Error Constant X1 X2 X3 40.28 1.36 12.03 1.65 0.121.22 6.481.54 Write the regression equation....
7. Multiple regression analysis is used to study how an individual's income (y, in thousands of...
7. Multiple regression analysis is used to study how an individual's income (y, in thousands of dollars) is influenced by age (x1, in years), level of education (22, ranging from 1 to 5), and the individual's gender (23, where 0 = female and 1 = male). The following shows parts of the regression output for a sample of 20 individuals. 21 Variable Coefficient 0.63 0.92 -0.51 S Sres = 112, SSexp = 84 Standard Error 0.09 0.19 0.92 23 (a)...
Using the Excel’s Regression Tool, develop the estimated regression equation to show how income (y annual...
Using the Excel’s Regression Tool, develop the estimated regression equation to show how income (y annual income in $1000s) is related to the independent variables education (x1 level of education attained in number of years), age (x2 in years), and gender x3 dummy variable, 1= female, 0 = male. Develop the dummy variable for the gender variable first. Use the t test to test whether each of the coefficients obtained in part (a) are significant at .05 level of significance....
Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1000s) of...
Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (xx) (o if O male and 1 if female). 9 - 30 +0.73 +372 Also provided are SST - 1200 and SSE - 384. The multiple coefficient of determination is . O 6.32 O c.so
Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 3 2432.5 810.84 44.44 ...
Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 3 2432.5 810.84 44.44 0.000 Horsepower (X1) 1 234.5 234.54 12.85 0.001 Weight (X2) 1 147.2 147.17 8.07 0.007 Transmission(X3) 1 144.9 144.88 7.94 0.007 Error 46 839.3 18.25 Total 49 3271.8 Does the regression coefficient of transmission type have a practical meaning in the context of this problem? Show (here) that this coefficient is numerically equal to SSR/SST. Specifically in this problem,...
Consider a multiple regression model of the dependent variable y on independent variables x1, X2, X3, and x4: Using data with n 60 observations for each of the variables, a student obtains the follow...
Consider a multiple regression model of the dependent variable y on independent variables x1, X2, X3, and x4: Using data with n 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: y0.35 0.58x1 + 0.45x2-0.25x3 - 0.10x4 He would like to conduct significance tests for a multiple regression relationship. He uses the F test to determine whether a significant relationship exists between the dependent variable and He uses the t...
The following is a partial result of Multiple Regression analysis conducted in Excel. Predictor Coefficients Standard...
The following is a partial result of Multiple Regression analysis conducted in Excel. Predictor Coefficients Standard Error t Statistic p-value Intercept -139.61 2548.99 -0.05 0.157154 x1 4.25 22.25 1.08 0.005682 x2 3.10 17.45 1.87 0.03869 x3 15.18 11.88 1.03 0.00002 Specify the following: Regression Equation: Which independent/predictor variables are statistically significant at α = 0.01 and Why?
4. Testing for significance Aa Aa Consider a multiple regression model of the dependent variable y on independent variables x1, x2, X3, and x4: Using data with n = 60 observations for each of the var...
4. Testing for significance Aa Aa Consider a multiple regression model of the dependent variable y on independent variables x1, x2, X3, and x4: Using data with n = 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: 0.04 + 0.28X1 + 0.84X2-0.06x3 + 0.14x4 y She would like to conduct significance tests for a multiple regression relationship. She uses the F test to determine whether a significant relationship exists...
You may need to use the appropriate technology to answer this question. In a regression analysis ...
You may need to use the appropriate technology to answer this question. In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ = 25.2 + 5.5x1 For this estimated regression equation SST = 1,550 and SSE = 550. (a) At α = 0.05, test whether x1 is significant. State the null and alternative hypotheses. H0: β1 = 0 Ha: β1 ≠ 0H0: β0 = 0 Ha: β0 ≠ 0 H0: β1 ≠ 0 Ha: β1...
11. (25 points) A multiple regression analysis is conducted to determine factors that relate to the success of sales associates. The regression is conducted between annual sales (Y in $1,000s), years of experience gion (X3; zero representing USA and 1 representing Canada) was performed on a sample of 29 people, and the following results were obtamed where SSR 84 60 amd SSE 57.5. Standard Coefficient Error Constant X1 X2 X3 40.28 1.36 12.03 1.65 0.121.22 6.481.54 Write the regression equation....
7. Multiple regression analysis is used to study how an individual's income (y, in thousands of dollars) is influenced by age (x1, in years), level of education (22, ranging from 1 to 5), and the individual's gender (23, where 0 = female and 1 = male). The following shows parts of the regression output for a sample of 20 individuals. 21 Variable Coefficient 0.63 0.92 -0.51 S Sres = 112, SSexp = 84 Standard Error 0.09 0.19 0.92 23 (a)...
Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (xx) (o if O male and 1 if female). 9 - 30 +0.73 +372 Also provided are SST - 1200 and SSE - 384. The multiple coefficient of determination is . O 6.32 O c.so
Consider a multiple regression model of the dependent variable y on independent variables x1, X2, X3, and x4: Using data with n 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: y0.35 0.58x1 + 0.45x2-0.25x3 - 0.10x4 He would like to conduct significance tests for a multiple regression relationship. He uses the F test to determine whether a significant relationship exists between the dependent variable and He uses the t...
4. Testing for significance Aa Aa Consider a multiple regression model of the dependent variable y on independent variables x1, x2, X3, and x4: Using data with n = 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: 0.04 + 0.28X1 + 0.84X2-0.06x3 + 0.14x4 y She would like to conduct significance tests for a multiple regression relationship. She uses the F test to determine whether a significant relationship exists...
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