Econometrics: MULTIPLE REGRESSION: ESTIMATION AND HYPOTHESIS TESTING CM FLR PGNP
ID: 3157460 • Letter: E
Question
Econometrics: MULTIPLE REGRESSION: ESTIMATION AND HYPOTHESIS TESTING
CM
FLR
PGNP
TFR
128
37
1870
6.66
204
22
130
6.15
202
16
310
7
197
65
570
6.25
96
76
2050
3.81
209
26
200
6.44
170
45
670
6.19
240
29
300
5.89
241
11
120
5.89
55
55
290
2.36
75
87
1180
3.93
129
55
900
5.99
24
93
1730
3.5
165
31
1150
7.41
94
77
1160
4.21
96
80
1270
5
148
30
580
5.27
98
69
660
5.21
161
43
420
6.5
118
47
1080
6.12
269
17
290
6.19
189
35
270
5.05
126
58
560
6.16
12
81
4240
1.8
167
29
240
4.75
135
65
430
4.1
107
87
3020
6.66
72
63
1420
7.28
128
49
420
8.12
27
63
19830
5.23
152
84
420
5.79
224
23
530
6.5
142
50
8640
7.17
104
62
350
6.6
287
31
230
7
41
66
1620
3.91
312
11
190
6.7
77
88
2090
4.2
142
22
900
5.43
262
22
230
6.5
215
12
140
6.25
246
9
330
7.1
191
31
1010
7.1
182
19
300
7
37
88
1730
3.46
103
35
780
5.66
67
85
1300
4.82
143
78
930
5
83
85
690
4.74
223
33
200
8.49
240
19
450
6.5
312
21
280
6.5
12
79
4430
1.69
52
83
270
3.25
79
43
1340
7.17
61
88
670
3.52
168
28
410
6.09
28
95
4370
2.86
121
41
1310
4.88
115
62
1470
3.89
186
45
300
6.9
47
85
3630
4.1
178
45
220
6.09
142
67
560
7.2
CM
FLR
PGNP
TFR
128
37
1870
6.66
204
22
130
6.15
202
16
310
7
197
65
570
6.25
96
76
2050
3.81
209
26
200
6.44
170
45
670
6.19
240
29
300
5.89
241
11
120
5.89
55
55
290
2.36
75
87
1180
3.93
129
55
900
5.99
24
93
1730
3.5
165
31
1150
7.41
94
77
1160
4.21
96
80
1270
5
148
30
580
5.27
98
69
660
5.21
161
43
420
6.5
118
47
1080
6.12
269
17
290
6.19
189
35
270
5.05
126
58
560
6.16
12
81
4240
1.8
167
29
240
4.75
135
65
430
4.1
107
87
3020
6.66
72
63
1420
7.28
128
49
420
8.12
27
63
19830
5.23
152
84
420
5.79
224
23
530
6.5
142
50
8640
7.17
104
62
350
6.6
287
31
230
7
41
66
1620
3.91
312
11
190
6.7
77
88
2090
4.2
142
22
900
5.43
262
22
230
6.5
215
12
140
6.25
246
9
330
7.1
191
31
1010
7.1
182
19
300
7
37
88
1730
3.46
103
35
780
5.66
67
85
1300
4.82
143
78
930
5
83
85
690
4.74
223
33
200
8.49
240
19
450
6.5
312
21
280
6.5
12
79
4430
1.69
52
83
270
3.25
79
43
1340
7.17
61
88
670
3.52
168
28
410
6.09
28
95
4370
2.86
121
41
1310
4.88
115
62
1470
3.89
186
45
300
6.9
47
85
3630
4.1
178
45
220
6.09
142
67
560
7.2
4.14. Table 4-7 (found on the textbook's Web site) gives data on child mortality (CM), female literacy rate (FLR), per capita GNP (PGNP), and total fertility rate (TFR) for a group of 64 countries a. A priori, what is the expected relationship between CM and each of the other variables? b. Regress CM on FLR and obtain the usual regression results c. Regress CM on FLR and PGNP and obtain the usual results. d. Regress CM on FLR, PGNP, and TFR and obtain the usual results. Also e. Given the various regression results, which model would you choose and f. If the regression model in (d) is the correct model, but you estimate (a) or (b) g. Suppose you have regressed CM on FLR as in (b). How would you decide show the ANOVA table. why? or (c), what are the consequences? if it is worth adding the variables PGNP and TFR to the model? Which test would you use? Show the necessary calculationsExplanation / Answer
In the data set the following variables are recorded and namely child mortality (CM), female literacy rate (FLR), per capita GNP (PGNP) and total fertality rate (TFR) and number of sample is 64.
a.
On the basis of Prior information we assumed that all variables are linearly related i.e CM is linearly related with the other variables.
b.
Regress CMon FLR and regression results as follows , here we use the R- software
x<-read.csv(file.choose(),header=T)
CM<-x[,1]
FLR<-x[,2]
PGNP<-x[,3]
TFR<-x[,4]
> lm(CM~FLR)
Call:
lm(formula = CM ~ FLR)
Coefficients:
(Intercept) FLR
263.86 -2.39
> summary(lm(CM~FLR))
Call:
lm(formula = CM ~ FLR)
Residuals:
Min 1Q Median 3Q Max
-86.262 -25.453 0.357 22.591 98.337
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 263.8635 12.2250 21.58 <2e-16 ***
FLR -2.3905 0.2133 -11.21 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 44.02 on 62 degrees of freedom
Multiple R-squared: 0.6696, Adjusted R-squared: 0.6643
F-statistic: 125.6 on 1 and 62 DF, p-value: < 2.2e-16
c.
Regress CM on FLR and PGNP and regression result as follows
> lm(CM~FLR + PGNP)
Call:
lm(formula = CM ~ FLR + PGNP)
Coefficients:
(Intercept) FLR PGNP
263.641586 -2.231586 -0.005647
> summary(lm(CM~FLR+PGNP))
Call:
lm(formula = CM ~ FLR + PGNP)
Residuals:
Min 1Q Median 3Q Max
-84.267 -24.363 0.709 19.455 96.803
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 263.641586 11.593179 22.741 < 2e-16 ***
FLR -2.231586 0.209947 -10.629 1.64e-15 ***
PGNP -0.005647 0.002003 -2.819 0.00649 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 41.75 on 61 degrees of freedom
Multiple R-squared: 0.7077, Adjusted R-squared: 0.6981
F-statistic: 73.83 on 2 and 61 DF, p-value: < 2.2e-16
d.
Regress CM on FLR, PGNP and TFR and regression results with ANOVA Table
> lm(CM~FLR + PGNP+TFR)
Call:
lm(formula = CM ~ FLR + PGNP + TFR)
Coefficients:
(Intercept) FLR PGNP TFR
168.306690 -1.768029 -0.005511 12.868636
> summary(lm(CM~FLR+PGNP+TFR))
Call:
lm(formula = CM ~ FLR + PGNP + TFR)
Residuals:
Min 1Q Median 3Q Max
-98.17 -18.56 3.32 17.12 98.72
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 168.306690 32.891655 5.117 3.44e-06 ***
FLR -1.768029 0.248017 -7.129 1.51e-09 ***
PGNP -0.005511 0.001878 -2.934 0.00473 **
TFR 12.868636 4.190533 3.071 0.00320 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 39.13 on 60 degrees of freedom
Multiple R-squared: 0.7474, Adjusted R-squared: 0.7347
F-statistic: 59.17 on 3 and 60 DF, p-value: < 2.2e-16
e.
Among the following model model - 3 ( d) be the best regression fitting model, multiple regression coefficient of this model is 0.7474 which is greater than other two model (model-1 (0.6696) and model - 2 (0.7077).
f.
In the fitting of the multiple regression model the model - 3 i.e d is the best model and during the fitting the model as variable was added in the model the value of multiple regression coefficent is also increases, and finally model -3 be have maximum multiple regression coefficient value.
g.
For the independent variable selection in the multiple regression, we use the t- test, at first we select that variable which is highely correlated with dependent variable. here CM is dependent variable and suppose that FLR already came in the regression model and i want to add the another variable PGNP and TFR in the model for that we use the t- test of correlation test, if it is insignificant then came in the model otherwise outside the model.
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