Homework Answers
a)
| Source | df | SS | MS | F |
| regression | 1 | 136.94 | 136.9400 | 34.5725 |
| error | 21 | 83.18 | 3.9610 | |
| total | 22 | 220.12 |
b)
s=√MSE =1.9902
c)
% of variance that can be explained =SSR/SST = 62.2115
d)
test statistic =sqrt(f)= 5.8798
E)
t* =3.8193
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A simple linear regression (linear regression with only one predictor) analysis was carried out using a...
Consider the following partial computer output from a simple linear regression analysis. Predictor Coef SE Coef...
Consider the following partial computer output from a simple linear regression analysis. Predictor Coef SE Coef T P 4.8615 9.35 0.5201 0.000 Constant -0.34655 0.05866 Independent Var S = .4862R-Sq| Analysis of Variance SS MS Source DF F Regression 1 34.90 Residual Error 13 Total 14 11.3240 Calculate the MSE
Consider the following partial computer output from a simple linear regression analysis. Predictor Coef SE Coef T P 4.8615 9.35 0.5201 0.000 Constant -0.34655 0.05866 Independent Var S = .4862R-Sq|...
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for...
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for i = 1, ...,n, where are i.i.d. following N (0, o2) distribution. It is known that x4 n, and x = 0, otherwise. Denote by n2 = n - ni, Ji = 1 yi, and j2 = 1 1. for i = 1, ... ,n1 < n2 Lizn1+1 Yi. n1 Zi=1 1. Find the least squares estimators of Bo and 31, in terms of...
Consider the following partial computer output from a simple linear regression analysis. P Predictor Coef SE...
Consider the following partial computer output from a simple linear regression analysis. P Predictor Coef SE Coef T Constant 9.35 0.000 4.8615 0.5201 0.05866 Independent Var -0.34655 S=4862R-Sq. Analysis of Variance MS DF SS F Source 1 34.90 Regression 13 Residual Error 14 11.3240 Total What is the predicted value of ywhen x 9.00?
(13 points) Suppose you have a simple linear regression model such that Y; = Bo +...
(13 points) Suppose you have a simple linear regression model such that Y; = Bo + B18: +€4 with and N(0,0%) Call: 1m (formula - y - x) Formula: F=MSR/MSE, R2 = SSR/SSTO ANOVA decomposition: SSTOSSE + SSR Residuals: Min 1Q Modian -2.16313 -0.64507 -0.06586 Max 30 0.62479 3.00517 Coefficients: Estimate Std. Error t value Pr(> It) (Intercept) 8.00967 0.36529 21.93 -0.62009 0.04245 -14.61 <2e-16 ... <2e-16 .. Signif. codes: ****' 0.001 '** 0.01 '* 0.05 0.1'' 1 Residual standard...
For the statement of one predictor simple linear regression model. True or False. "Covariance between ei...
For the statement of one predictor simple linear regression model. True or False. "Covariance between ei and ej is zero but yi and yj have non-zero covariance. "
how would I figure out the best regression model? Least Squares Linear Regression of Rent Predictor...
how would I figure out the best regression model?
Least Squares Linear Regression of Rent Predictor Variables Constant Size Location Coefficient 1260.79 0.08977 191.625 Std Error 455.277 0.42423 194.769 T 2.77 0.21 0.98 P 0.0080 0.8333 0.3302 VIF 0.0 1.0 1.0 Mean Square Error (MSE) Standard Deviation 458838 677.376 RS Adjusted R AICC PRESS 0.0234 -0.0182 657.62 2.38E+07 DF F 0.56 P 0.5738 2 Source Regression Residual Total MS 257878 458838 SS 515756 2.157E+07 2.208E+07 47 49 45 M M...
A used car salesman wants to explain car price ($1,000s) using car age (years). A sample...
A used car salesman wants to explain car price ($1,000s) using car age (years). A sample of midsized sedans was obtained. The output from a simple linear regression on the data is below. Parameter Estimate Std. Err. DF T-Stat P-value Intercept 17.370 1.448 8 11.31 0.000 Slope - 1.2283 0.2130 8 -5.77 0.001 Analysis of variance table for regression model: Source DF SS MS F-stat P-value Model 1 138.79 138.79 33.26 0.001 Error 8 29.21 4.17 Total 9 168.00 S...
eBook Video In a regression analysis involving 30 observations, the following estimated regression equation was obtained....
eBook Video In a regression analysis involving 30 observations, the following estimated regression equation was obtained. 17.6+3.8z-2.3z +7.6z, +2.7z For this estimated regression equation SST- 1805 and SSR- 1,764. a. At a 0.05, test the significance of the relashionship among the variables. SSE (to 1 decimal, if necessary) MSR (to 1 decimal, if necessary) MSE (to 2 decimal if necessary) What is the value of the F test statistic (to 1 decimal)? Use Table 4 in Appendix B. What is...
A multiple regression analysis produced the following tables: Predictor Intercept Xi x2 Coefficients 616.6849 -3.33833 1.780075...
A multiple regression analysis produced the following
tables:
Predictor Intercept Xi x2 Coefficients 616.6849 -3.33833 1.780075 Standard Error 154.5534 2.333548 0.335605 t statistic 3.990108 -1.43058 5.30407 p value 0.000947 0.170675 5.83E-05 Source Regression Residual Total df 2 15 17 SS 121783 61876.68 183659.6 MS 60891.48 4125.112 p value 0.000286 F 14.76117 Using a = 0.01 to test the null hypothesis Ho: B1 = B2 = 0, the critical F value is 8.68 6.36 8.40 O 6.11 O 3.36
The following table is the output of multiple linear regression analysis. a. Use the table to...
The following table is the output of multiple linear regression
analysis.
a. Use the table to report the F statistic. What is its degree of
freedom? What is the number of observations.
b. Find the p-value related to F on the computer output and report
its value. Using the p-value, test the significance of the
regression model at the .10, .05, .01, and .001 levels of
significance. What do you conclude?
Please show work and explain each step!
df ANOVA...
Consider the following partial computer output from a simple linear regression analysis. Predictor Coef SE Coef T P 4.8615 9.35 0.5201 0.000 Constant -0.34655 0.05866 Independent Var S = .4862R-Sq| Analysis of Variance SS MS Source DF F Regression 1 34.90 Residual Error 13 Total 14 11.3240 Calculate the MSE
Consider the following partial computer output from a simple linear regression analysis. Predictor Coef SE Coef T P 4.8615 9.35 0.5201 0.000 Constant -0.34655 0.05866 Independent Var S = .4862R-Sq|...
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for i = 1, ...,n, where are i.i.d. following N (0, o2) distribution. It is known that x4 n, and x = 0, otherwise. Denote by n2 = n - ni, Ji = 1 yi, and j2 = 1 1. for i = 1, ... ,n1 < n2 Lizn1+1 Yi. n1 Zi=1 1. Find the least squares estimators of Bo and 31, in terms of...
Consider the following partial computer output from a simple linear regression analysis. P Predictor Coef SE Coef T Constant 9.35 0.000 4.8615 0.5201 0.05866 Independent Var -0.34655 S=4862R-Sq. Analysis of Variance MS DF SS F Source 1 34.90 Regression 13 Residual Error 14 11.3240 Total What is the predicted value of ywhen x 9.00?
(13 points) Suppose you have a simple linear regression model such that Y; = Bo + B18: +€4 with and N(0,0%) Call: 1m (formula - y - x) Formula: F=MSR/MSE, R2 = SSR/SSTO ANOVA decomposition: SSTOSSE + SSR Residuals: Min 1Q Modian -2.16313 -0.64507 -0.06586 Max 30 0.62479 3.00517 Coefficients: Estimate Std. Error t value Pr(> It) (Intercept) 8.00967 0.36529 21.93 -0.62009 0.04245 -14.61 <2e-16 ... <2e-16 .. Signif. codes: ****' 0.001 '** 0.01 '* 0.05 0.1'' 1 Residual standard...
how would I figure out the best regression model?
Least Squares Linear Regression of Rent Predictor Variables Constant Size Location Coefficient 1260.79 0.08977 191.625 Std Error 455.277 0.42423 194.769 T 2.77 0.21 0.98 P 0.0080 0.8333 0.3302 VIF 0.0 1.0 1.0 Mean Square Error (MSE) Standard Deviation 458838 677.376 RS Adjusted R AICC PRESS 0.0234 -0.0182 657.62 2.38E+07 DF F 0.56 P 0.5738 2 Source Regression Residual Total MS 257878 458838 SS 515756 2.157E+07 2.208E+07 47 49 45 M M...
A used car salesman wants to explain car price ($1,000s) using car age (years). A sample of midsized sedans was obtained. The output from a simple linear regression on the data is below. Parameter Estimate Std. Err. DF T-Stat P-value Intercept 17.370 1.448 8 11.31 0.000 Slope - 1.2283 0.2130 8 -5.77 0.001 Analysis of variance table for regression model: Source DF SS MS F-stat P-value Model 1 138.79 138.79 33.26 0.001 Error 8 29.21 4.17 Total 9 168.00 S...
eBook Video In a regression analysis involving 30 observations, the following estimated regression equation was obtained. 17.6+3.8z-2.3z +7.6z, +2.7z For this estimated regression equation SST- 1805 and SSR- 1,764. a. At a 0.05, test the significance of the relashionship among the variables. SSE (to 1 decimal, if necessary) MSR (to 1 decimal, if necessary) MSE (to 2 decimal if necessary) What is the value of the F test statistic (to 1 decimal)? Use Table 4 in Appendix B. What is...
A multiple regression analysis produced the following
tables:
Predictor Intercept Xi x2 Coefficients 616.6849 -3.33833 1.780075 Standard Error 154.5534 2.333548 0.335605 t statistic 3.990108 -1.43058 5.30407 p value 0.000947 0.170675 5.83E-05 Source Regression Residual Total df 2 15 17 SS 121783 61876.68 183659.6 MS 60891.48 4125.112 p value 0.000286 F 14.76117 Using a = 0.01 to test the null hypothesis Ho: B1 = B2 = 0, the critical F value is 8.68 6.36 8.40 O 6.11 O 3.36
The following table is the output of multiple linear regression
analysis.
a. Use the table to report the F statistic. What is its degree of
freedom? What is the number of observations.
b. Find the p-value related to F on the computer output and report
its value. Using the p-value, test the significance of the
regression model at the .10, .05, .01, and .001 levels of
significance. What do you conclude?
Please show work and explain each step!
df ANOVA...
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