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?
The independent/predictor variables X1 and X3 are statistically significant at α = 0.01 because the p-value of t statistic is less than 0.01
The following is a partial result of Multiple Regression analysis conducted in Excel. Predictor Coefficients Standard...
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...
A multiple regression analysis produced the following tables: Predictor Intercept xi x2 Coefficients 624.5369 8.569122 4.736515 Standard Error 78.49712 1.652255 0.699194 t statistic 7.956176 5.186319 6.774248 p value 6.88E-06 0.000301 3.06E-05 Source Regression Residual Total df 2 11 13 SS 1660914 156637.5 1817552 MS 830457.1 14239.77 F 58.31956 p value 1.4E-06 For x1= 30 and x2 = 100, the predicted value of y is 753.77 O 1,173.00 O 1,355.26 615.13 6153.13
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
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....
Consider the following Excel multiple regression of output of Total Sales on the (c) other (predictor) variables. Provide some important arguments about the fitted multiple regression model. (Give one argument about each of the three main outputs.) [4 marks] SUMMARY OUTPUT Regression Statistics Multiple R 0.9870 R Square Adjusted R Square 0.9741 0.9721 Standard Error 116.2766 Observations 43 ANOVA Significance F df SS MS F Regression 19817036.22 6605678.74 488.58 5.82876E-31 Residual 527289.46 39 13520.24 Total 42 20344325.68 P-value Coefficients Standard...
A multiple regression analysis produced the following tables. Coefficients Standard Error t Statistic p-value Intercept 1411.876 762.1533 1.852483 0.074919 x1 35.18215 96.8433 0.363289 0.719218 x12 7.721648 3.007943 2.567086 0.016115 df SS MS F Regression 2 58567032 29283516 57.34861 Residual 25 12765573 510622.9 Total 27 71332605 The regression equation for this analysis is ____________. Select one: A. y = 762.1533 + 96.8433 x1 + 3.007943 x12 B. y = 1411.876 + 762.1533 x1 + 1.852483 x12 C. y = 1411.876 +...
Consider a multiple linear regression model Y; = Bo + B1Xi1 + B22:2 + 33213 + Blog(x14) + Ej. We have the following statistics for the regression Call: 1m formula = y “ x1 + x2 + x3 + log(x4) Coefficients: Estimate Std. Error t value Pr(>1t|) (Intercept) 154.1928 194.9062 0.791 0.432938 x1 -4.2280 2.0301 -2.083 0.042873 * x2 -6.1353 2.1936 -2.797 0.007508 ** x3 0.4719 0.1285 3.672 0.000626 *** x4 26.7552 9.3374 2.865 0.006259 ** Signif. codes: O '***'...
Consider a multiple linear regression model Y; = Bo + B1Xi1 + B22:2 + 33213 + Blog(x14) + Ej. We have the following statistics for the regression Call: 1m formula = y “ x1 + x2 + x3 + log(x4) Coefficients: Estimate Std. Error t value Pr(>1t|) (Intercept) 154.1928 194.9062 0.791 0.432938 x1 -4.2280 2.0301 -2.083 0.042873 * x2 -6.1353 2.1936 -2.797 0.007508 ** x3 0.4719 0.1285 3.672 0.000626 *** x4 26.7552 9.3374 2.865 0.006259 ** Signif. codes: O '***'...
(a) The following is taken from the output generated by an Excel analysis of expenditure data using multiple regression: Regression Statistics Multiple R 0.9280 0.8611 0.8365 Adjusted R2 Standard Error.1488 Observations21 ANOVA Source Regression Residual Total df MS Significance of F 1.66E-07 3 308.68 35.117 102.893 2.930 17 20 358.49 49.81 Coefficient Standard Error 6.2000 0.7260 0.7260 0.9500 t Stat 3.7097 0.2755 -2.0523 0.5158 23.00 0.20 Intercept X2 X3 0.49 (i) Find the limits of the 95 percent confidence interval...
For the following question (#19 and #20), please use the following multiple regression output. The dependent variable is Home Price: ($) the independent variables are Number of Bedrooms, Size (square footage), and Pool (0 = no pool, 1 = pool). 19: Which statement is correct? SUMMARY OUTPUT A: The R square of 571 is the best goodness of fit statistic to use for multiple regression analyses. B: The Number of Bedrooms is not a significant predictor variable. Regression Statistics Multiple...