Question

In: Economics

Using an interval, predict the particular value of the dependent variable for a selected value of...

  1. Using an interval, predict the particular value of the dependent variable for a selected value of the independent variable. Interpret this interval.
  2. What can be said about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain.
    • In an attempt to improve the model, use a multiple regression model to predict the dependent variable .Y, based on all of the independent variables. X1, X2, and X3.
  3. Using Excel, run the multiple regression analysis using the designated dependent and three independent variables. State the equation for this multiple regression model.
  4. Perform the Global Test for Utility (F-Test). Explain the conclusion.
  5. Perform the t-test on each independent variable. Explain the conclusions and clearly state how the analysis should proceed. In particular, which independent variables should be kept and which should be discarded. If any independent variables are to be discarded, re-run the multiple regression, including only the significant independent variables, and summarize results with discussion of analysis.
  6. Is this multiple regression model better than the linear model generated in parts 1-10? Explain.
  7. All DeVry University policies are in effect, including the plagiarism policy.
  8. Part C report is due by the end of Week 7.
  9. Part C is worth 100 total points. See grading rubric below.
Sales (Y) Calls (X1) Time (X2) Years (X3) Type
47 167 12.9 5 ONLINE
43 137 16.6 4 NONE
48 164 14.7 3 NONE
46 182 13.2 3 ONLINE
42 183 14.4 2 ONLINE
51 183 11.4 2 ONLINE
34 122 20.4 3 NONE
30 175 14.3 3 GROUP
46 160 12.9 1 GROUP
38 145 15.6 3 NONE
34 184 12.5 4 GROUP
44 144 15.3 0 GROUP
44 136 17.2 2 GROUP
40 201 13.1 2 ONLINE
45 148 16.3 0 ONLINE
43 164 13.1 3 ONLINE
39 127 17.1 2 ONLINE
46 148 15.5 1 GROUP
39 131 18.4 1 GROUP
35 188 18.2 2 ONLINE
43 153 17.3 1 NONE
44 145 15.8 1 NONE
40 132 12.8 1 NONE
41 120 17.7 0 NONE
40 148 15.2 3 GROUP
36 173 14.3 4 GROUP
48 191 13.6 1 GROUP
46 161 16.6 3 ONLINE
42 153 14.9 3 GROUP
47 173 14.6 2 ONLINE
43 164 15.2 0 ONLINE
39 181 14.7 3 ONLINE
48 163 15.5 3 GROUP
52 187 12.5 2 ONLINE
48 142 14.8 0 NONE
41 137 16.7 1 NONE
47 167 16.1 5 ONLINE
43 173 12.8 0 ONLINE
45 152 17.1 3 GROUP
43 150 15.3 2 GROUP
39 147 13.6 3 GROUP
41 133 15.9 2 NONE
48 173 17.4 0 ONLINE
44 160 14.1 4 NONE
44 133 19.2 3 GROUP
38 127 18.5 1 GROUP
34 132 18.2 4 NONE
48 182 14.1 4 ONLINE
44 165 14.2 5 GROUP
40 158 15.6 2 ONLINE
52 181 11.8 2 ONLINE
38 139 12.2 1 NONE
34 160 13.1 1 ONLINE
47 166 13.8 3 ONLINE
41 138 16.1 2 NONE
37 171 11.7 2 GROUP
47 174 13.8 2 GROUP
40 146 18.2 2 GROUP
36 158 17.5 1 GROUP
50 162 15.6 2 ONLINE
41 158 13.8 4 GROUP
37 192 13.7 3 ONLINE
48 152 19.9 2 ONLINE
42 154 13.6 3 ONLINE
38 163 10.8 4 GROUP
50 172 11.1 1 ONLINE
44 174 18.5 2 GROUP
40 192 12.7 1 ONLINE
53 183 11.4 4 ONLINE
46 170 14.2 2 ONLINE
42 191 14.2 0 ONLINE
41 148 14.8 1 GROUP
41 155 14.8 2 GROUP
37 163 14.4 2 ONLINE
45 165 16.4 1 GROUP
53 174 15.1 1 ONLINE
49 181 11.6 2 NONE
52 175 12.3 1 NONE
40 139 15.7 2 NONE
36 162 18.4 2 ONLINE
42 148 13.7 2 NONE
41 147 16.8 2 GROUP
37 189 12.7 1 ONLINE
51 193 12.1 2 ONLINE
39 148 14.4 4 GROUP
35 149 19.3 2 NONE
49 187 14.3 2 ONLINE
40 135 19.5 3 GROUP
36 204 12.1 1 ONLINE
45 155 11.6 3 GROUP
37 128 19.7 2 NONE
33 164 15.9 3 ONLINE
45 151 13.6 1 GROUP
46 174 16.6 2 GROUP
42 160 16.5 3 GROUP
45 153 13.4 1 GROUP
45 152 21.8 0 ONLINE
41 173 15.4 1 ONLINE
48 169 14.8 0 ONLINE
38 142 17.9 3 NONE

Solutions

Expert Solution

Y = 42.4108 + 0.0453X1 -0.3885X2 - 0.5703X3

Regression Analysis
Regression Statistics
Multiple R 0.3328
R Square 0.1108
Adjusted R Square 0.0830
Standard Error 4.8233
Observations 100
ANOVA
df SS MS F Significance F
Regression 3 278.1889 92.7296 3.9859 0.0101
Residual 96 2233.3711 23.2643
Total 99 2511.5600
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95% Upper 95%
Intercept 42.4108 7.8113 5.4294 0.0000 26.9055 57.9162 26.9055 57.9162
Calls (X1) 0.0453 0.0306 1.4774 0.1429 -0.0156 0.1061 -0.0156 0.1061
Time (X2) -0.3885 0.2509 -1.5482 0.1249 -0.8865 0.1096 -0.8865 0.1096
Years (X3) -0.5703 0.3936 -1.4490 0.1506 -1.3515 0.2110 -1.3515 0.2110

Rather than testing each β individually, we use a global test that encompasses all β’s and test the following overall hypothesis:

H0 : β1 = β2 = ... = βk = 0

Ha : at least one βj 0.

The test statistic to test this hypothesis is called F−statistic and is calculated as:

Putting all values from above ANOVA regression, we get :

F = 3.9874

F (3,96) at = 5% is 2.6993


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Dependent Variable: BVPS_FSC                                     &nbsp
Dependent Variable: BVPS_FSC                                           Method: Least Squares                                                Date: 07/25/18   Time: 12:06                                      Sample (adjusted): 4/01/1998 4/01/2013                                             Included observations: 15 after adjustments                                                                                         Variable           Coefficient       Std. Error        t-Statistic         Prob.                                                  C                     3.316771        5.621129         0.590054         0.5714 CET_FSC       0.013773         0.021733         0.633729         0.5439 CR_FSC         0.489317         3.034456         0.161254         0.8759 CTR_FSC       0.008914         0.008949         0.996106         0.3484 ROA_FSC      -2.286163        1.433001         -1.595368        0.1493 ROE_FSC       0.759472         0.474621         1.600166         0.1482 ROI_FSC        0.261457         0.198688         1.315919         0.2247                                                  R-squared                     0.360769            Mean dependent var           6.687333 Adjusted R-squared    -0.118654           S.D. dependent var             1.987921 S.E. of regression        2.102553            Akaike info criterion           4.628907 Sum squared resid       35.36584            Schwarz criterion                4.959330 Log likelihood           -27.71680             Hannan-Quinn criter.          4.625387 F-statistic                     0.752506             Durbin-Watson stat             0.637955 Prob(F-statistic)          0.625229                                  1. discuss in detail the above data
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