The degrees of freedom for the sum of squares explained by the regression (SSR) are:
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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 | |||
[row intentionally left blank] | ||||
Coefficients | Standard Error |
|||
Intercept | 12.924 | 4.425 | ||
x1 | -3.682 | 2.630 | ||
x2 | 45.216 | 12.560 |
Refer to Exhibit 3. The degrees of freedom for the sum of squares explained by the regression (SSR) are:
2
13
15
3
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- Interpret the estimated education coefficient. Is the estimate of the constant statistically significant at the 5% level? Explain how you reached this conclusion. Imagine you want to test with an F-test whether the effect of married and nonwhite are jointly significantly different from zero. Write down the null and alternative hypothesis for such a testUse the given information about sums of squares and sample size for a linear model to fill in all values in the analysis of variance for regression table below. SSModel = 250 with SSTotal = 3000 and a sample size of n = Round your answer for the p-value to four decimal places, and all other answers to three decimal places, if necessary. Source Model Error Total i df 100. SS MS F-statistic i p-value7) Below is a multiple regression in which the dependent variable is market value of houses and the independent variables are the age of the house and square footage of the house. The regression was estimated for 42 houses. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total df 2 39 41 0.745495 0.555762 0.532981 7211.848 42 SS 2537650171 2028419591 4566069762 Coefficients Standard Error MS 1.27E+09 52010759 F 24.39544 Significance F 1.3443E-07 Upper 95% t Stat P-value Lower 95% Intercept 47331.38 13884.34664 3.408974 0.001528 19247.6673 House Age -825.161 607.3128421 -1.35871 0.182046 -2053.5662 Square Feet 40.91107 6.696523994 6.109299 3.65E-07 27.3660835 7A. What is the estimated regression equation for determining the market value of houses? 7B. Discuss tests of significance of the regression 7C. What percentage of the variation in the dependent variable, Market Value, is explained by the regression…
- For an ANOVA test of significance of a regression model with 10 regressor variables and 50 observations, what is the degree of freedom of the SSr? choices 11 10 39 49The summary output obtained from fitting the multiple regression are given below. Model Unstandardized Coefficients Standardized Sig. Coefficients B Std. Error Beta -3.512 (Constant) Education (years) -3019.226 859.789 .000 658.518 45.852 .581 14.362 .000 Gender -1615.440 253.239 -.249 -6.379 .000 Age (years) 45.008 10.469 .163 4.299 .000 Dependent Variable: Beginning Salary, Male=0 & Female=1. (a) Write down the estimated multiple regression model of the beginning salary on education, gender and age of employees of a company. (b) Interpret estimated regression coefficient values. (c) Find the predicted beginning salary for an employee who is 24 years old male and has 17 years of education.You may need to use the appropriate technology to answer this question. Following is a portion of the computer output for a regression analysis relating y = maintenance expense (dollars per month) to x = usage (hours per week) of a particular brand of computer terminal. Analysis of Variance SOURCE DF Adj SS Adj MS Regression 1 1575.76 1575.76 Error 8 349.14 43.64 Total 9 1924.90 Predictor Coef SE Coef Constant 6.1092 0.9361 X 0.8951 0.1490 Regression Equation Y = 6.1092 + 0.8951 X #1) Write the estimated regression equation. ŷ = #2) Find the value of the test statistic. (Round your answer to two decimal places.)Find the p-value. (Round your answer to three decimal places.) #3)Use the estimated regression equation to predict monthly maintenance expense (in dollars per month) for any terminal that is used 15 hoursper week. (Round your answer to the nearest cent.) $ _____per month
- 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 degrees of freedom for the sum of squares explained by the regression (SSR) are _____. a. 15 b. 13 c. 2 d. 3Read and analyze the result above using the Simple Linear Regression. Question: What is the effect size of the study? A. R square = 0.48; cannot be determined B. R square = 0.48; large effect C. R square = 0.48; medium effect D. R square = 0.48; small effectThe ANOVA summary table to the right is for a multiple regression model with six independent variables. Complete parts (a) through (e). Draw a conclusion. Choose the correct answer below. (3) Degrees of Source Freedom Regression Error Total 6 26 32 Sum of Squares 240 190 430 A. There is insufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is less than the critical value. O B. There is sufficient evidence of a significant linear relationship with at least one of the independent variables because the p-value is less than the level of significance. C. There is sufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is greater than the level of significance. D. There is insufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is greater than the critical value.
- A business is evaluating their advertising budget, and wishes to determine the relationship between advertising dollars spent and changes in revenue. Below is the output from their regression. SUMMARY OUTPUT Regression Statistics Multiple R 0.95 R Square 0.90 Adjusted R Square 0.82 Standard Error 0.82 Observations 8 ANOVA df SS MS F Significance F Regression 3 23.188 7.729 11.505 0.020 Residual 4 2.687 0.672 Total 7 25.875 Coefficients Std Error t Stat P-value Lower 95% Upper 95% Intercept 83.91 2.03 41.36 0.00 78.28 89.54 TV ($k) 1.96 0.48 4.10 0.01…Rewrite the regression model to include coefficients from your regression analysis output and then answer the following question What would be the company's loss if the significant variable(s) change per unit? SUMMARY OUTPUT Regression Statistics Multiple R 0.93082 R Square 0.866425 Adjusted R Square 0.85833 Standard Error 4108.993 Observations 36 ANOVA df SS MS F Significance F Regression 2 3.61E+09 1.81E+09 107.0261 3.75E-15 Residual 33 5.57E+08 16883824 Total 35 4.17E+09 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 3996.678 6603.651 0.605223 0.549171 -9438.55 17431.91 -9438.55 17431.91 X Variable 1 43.5364 3.589484 12.12887 1.05E-13 36.23354 50.83926 36.23354 50.83926 X Variable 2…Mm4