Question
In: Economics
Using an interval, predict the particular value of the dependent variable for a selected value of...
- Using an interval, predict the particular value of the dependent variable for a selected value of the independent variable. Interpret this interval.
- 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.
- Using Excel, run the multiple regression analysis using the designated dependent and three independent variables. State the equation for this multiple regression model.
- Perform the Global Test for Utility (F-Test). Explain the conclusion.
- 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.
- Is this multiple regression model better than the linear model generated in parts 1-10? Explain.
- All DeVry University policies are in effect, including the plagiarism policy.
- Part C report is due by the end of Week 7.
- 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
Rahul Sunny answered 8 months agoRelated Solutions
Construct a? 95% confidence interval for the dependent variable when x1=9 and x2=14?
y
10
11
15
15
20
24
27
32
x1
2
5
5
9
7
11
16
20
x2
16
10
13
10
2
8
7
4
Construct a? 95% confidence interval for the dependent variable
when x1=9 and x2=14?
The 95% prediction interval for the dependent varible when x1=9
and x2=14?
1. A researcher would like to predict the dependent variable YY from the two independent variables...
1. A researcher would like to predict the dependent variable YY
from the two independent variables X1X1 and X2X2 for a sample of
N=15N=15 subjects. Use multiple linear regression to calculate the
coefficient of multiple determination and test the significance of
the overall regression model. Use a significance level
α=0.05α=0.05.
X1X1
X2X2
YY
66.4
76.4
58
34.6
39
65.5
32.7
23.1
65.8
44.4
71.2
73.3
57.3
50.8
57.9
32.7
48
74.6
53.3
51.4
64.4
48.3
51.1
59.2
66.9
81.4
59.4...
A researcher would like to predict the dependent variable Y from the two independent variables X1...
A researcher would like to predict the dependent variable Y from
the two independent variables X1 and X2 for a sample of N=13
subjects. Use multiple linear regression to calculate the
coefficient of multiple determination and test statistics to assess
the significance of the regression model and partial slopes. Use a
significance level α=0.02.
X1X1
X2X2
YY
58
64.7
35.9
45
35.4
78.8
69.4
45.5
64.1
63.2
71.9
9
58
42.8
84.3
24.5
55.5
63.5
27.5
49.3
77.3
41.8
50.5...
A researcher would like to predict the dependent variable YY from the two independent variables X1X1...
A researcher would like to predict the dependent variable YY
from the two independent variables X1X1 and X2X2 for a sample of
N=11N=11 subjects. Use multiple linear regression to calculate the
coefficient of multiple determination and test statistics to assess
the significance of the regression model and partial slopes. Use a
significance level α=0.05α=0.05.
X1X1
X2X2
YY
55.3
51.1
56.2
72.1
51.6
76.6
35.2
41.7
51.8
70.4
58
47.9
51
71.6
39.8
66.6
60.4
61.9
61.9
48.9
63.4
46.8
54.3...
A researcher would like to predict the dependent variable YY from the two independent variables X1X1...
A researcher would like to predict the dependent variable YY
from the two independent variables X1X1 and X2X2 for a sample of
N=18N=18 subjects. Use multiple linear regression to calculate the
coefficient of multiple determination and test the significance of
the overall regression model. Use a significance level
α=0.05α=0.05.
X1X1
X2X2
YY
48.6
52.9
39.2
40.8
58.8
45.5
43.5
64.3
50.1
45.3
32.7
40.8
50.4
47.4
42.9
46.9
44.1
38.4
90.6
46.6
49.3
50.2
33.6
37.3
54.2
28.2
38.8
24.9...
A researcher would like to predict the dependent variable Y from the two independent variables X1...
A researcher would like to predict the dependent variable Y from
the two independent variables X1 and X2 for a sample of N=16
subjects. Use multiple linear regression to calculate the
coefficient of multiple determination and test the significance of
the overall regression model. Use a significance level α=0.05.
X1
X2
Y
48
42.3
47.1
36.3
58.7
65.4
43.4
40.2
63.6
49.5
37.9
45.6
45.5
37.2
50.8
40.6
64.7
42.4
42.5
46.7
63.1
42.7
40
35.8
55.8
10.6
52.1
40.9...
A researcher would like to predict the dependent variable Y from the two independent variables X1...
A researcher would like to predict the dependent variable Y from
the two independent variables X1 and X2 for a sample of N=12
subjects. Use multiple linear regression to calculate the
coefficient of multiple determination and test statistics to assess
the significance of the regression model and partial slopes. Use a
significance level α=0.05.
X1
X2 Y
34.4
26.4
59.4
53.7
38.3
90.4
72.8
43.2
71.3
25.4
21.2
64.5
75.9
46.5
71.1
60.4
27.9
72.6
28
56.4
29.9
40.1...
Linear regression is used to predict the value of one variable from another variable. Since it...
Linear regression is used to predict the value of one variable
from another variable. Since it is based on correlation, it cannot
provide causation. In addition, the strength of the relationship
between the two variables affects the ability to predict one
variable from the other variable; that is, the stronger the
relationship between the two variables, the better the ability to
do prediction.
What is one instance where you think linear regression would be
useful to you in your workplace...
Linear Regression Linear regression is used to predict the value of one variable from another variable....
Linear Regression
Linear regression is used to predict the value of one variable
from another variable. Since it is based on correlation, it cannot
provide causation. In addition, the strength of the relationship
between the two variables affects the ability to predict one
variable from the other variable; that is, the stronger the
relationship between the two variables, the better the ability to
do prediction.
What is one instance where you think linear regression
would be useful to you in...
Dependent Variable: BVPS_FSC  
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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