Question

Applied Econometrics

Use the dataset attached on blackboard and answer the following questions:

1. First study the simple linear regression model for the heart attack death rates, on the only basis of the number of phones. Determine whether the number of phone is associated significantly with the heart attack death rate.

2. Write the multiple linear regression model for the heart attack death rates on the basis of the number of phones and the proportion of saturated fat. Compute the associated least squares coefficient estimates.

3. Test whether at least one of the predictors number of phones, or proportion of saturated fat, is useful in predicting the heart attack death rate.

4. Compute the R2 statistic, and the residual standard error for the models in questions (b) and (c). Would you say that adding the proportion of saturated fat to the model significantly improves the accuracy?

5. Write the multiple linear regression model for the heart attack rates on the basis of the number of phones, the proportion of saturated fat, and the proportion of animal fat. Compute the associated least squares coefficient.

6. A country has the following features: 108 phones per 1000 inhabitants; 33% of saturated fat for men between the ages of 55 and 59; 7% of animal fat for men between the ages of 55 and 59.

Predict the heart attack death rate for men between the ages of 55 and 59 in that country.

7. Which coefficient estimates are significantly non-zero?

Iphones saturated animal deaths 81 124 49 181 31 38 17 20 39 30 29 35 31 23 21 80 24 78 52 152 75 45 10 43 69 4 17 12 13 45 24 43 38 72 16 10 63 170 125 12 221 23 37 15 16 17 18 19 20 21 38 25 38 52 39 52 97 254 38 39 89 23

Answer 1

a) Deaths = $\alpha$ + $\beta$ (Phones) + $\varepsilon$

OUTPUT FROM EXCEL :

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.469711
R Square	0.220628
Adjusted R Square	0.18166
Standard Error	17.46597
Observations	22
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1727.159	1727.159	5.661698	0.027409
Residual	20	6101.205	305.0602
Total	21	7828.364
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	46.23633	5.771113	8.011684	0.000	34.198	58.27466	34.198	58.27466
PHONES	0.120021	0.050441	2.379432	0.027409	0.014803	0.225239	0.014803	0.225239

Confidence interval is 95%

Since P values of both intercept term and Parameter for Phone is less than 0.05, we can say that there is a significant impact of no.of phones on deaths.

R² of the model is 0.22 i.e. 22% of variation in deaths is explained by phones.

b) Deaths =  $\alpha$ + $\beta$₁ (Phones) + $\beta$2 (saturated fats) + $\varepsilon$

EXCEL OUTPUT:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.489542
R Square	0.239651
Adjusted R Square	0.159614
Standard Error	17.69967
Observations	22
ANOVA
	df	SS	MS	F	Significance F
Regression	2	1876.075	938.0374	2.994262	0.074067
Residual	19	5952.289	313.2784
Total	21	7828.364
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	35.55464	16.56005	2.147013	0.044912	0.894065	70.21522	0.894065	70.21522
PHONES	0.07895	0.078495	1.005803	0.327149	-0.08534	0.243242	-0.08534	0.243242
SATURATED	0.470729	0.682757	0.689454	0.498872	-0.9583	1.899755	-0.9583	1.899755

$\alpha$ = 35.55

$\BETA$$\beta$₁ = 0.07

$\beta$₂ = 0.47

c) Neither of the coefficient is significant as P values are more than 0.05 for both variables.

d) R² is 0.23 i.e 23% of variation in deaths is explained by saturated fats and phones. So, no the model is not improved significantly by addition of saturated fat variable.

RESIDUAL OUTPUT
Observation	Predicted DEATHS	Residuals	Standard Residuals		sum resid.
1	60.87855	20.12145	1.195163		0.000
2	54.01581	0.984186	0.058458
3	67.73236	12.26764	0.728666
4	43.87284	-19.8728	-1.1804
5	46.70613	31.29387	1.858775
6	65.91353	-13.9135	-0.82643
7	55.59779	32.40221	1.924608
8	53.46911	-8.46911	-0.50304
9	55.42503	-5.42503	-0.32223
10	53.38421	15.61579	0.927538
11	47.72357	18.27643	1.085573
12	47.17686	-2.17686	-0.1293
13	40.58368	-16.5837	-0.98503
14	47.17092	-4.17092	-0.24774
15	57.94549	-19.9455	-1.18471
16	67.80537	4.194632	0.24915
17	63.31114	-22.3111	-1.32522
18	48.27028	-10.2703	-0.61003
19	71.36111	-19.3611	-1.15
20	64.58921	-12.5892	-0.74777
21	61.10053	4.899466	0.291016
22	73.96647	15.03353	0.892953

Sum of residual square is 0.

e) Deaths =  $\alpha$ + $\beta$₁ (Phones) + $\beta$2 (saturated fats) +  $\beta$₃(Animal fats) + $\varepsilon$

EXCEL OUTPUT

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.633586
R Square	0.401432
Adjusted R Square	0.30167
Standard Error	16.13452
Observations	22
ANOVA
	df	SS	MS	F	Significance F
Regression	3	3142.553	1047.518	4.023917	0.023569
Residual	18	4685.811	260.3228
Total	21	7828.364
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	23.99957	15.97887	1.501957	0.150448	-9.57079	57.56992	-9.57079	57.56992
PHONES	-0.00617	0.081298	-0.07594	0.940308	-0.17697	0.164627	-0.17697	0.164627
SATURATED	-0.47987	0.757034	-0.63388	0.534132	-2.07034	1.1106	-2.07034	1.1106
ANIMAL	8.4835	3.846205	2.205681	0.040646	0.402924	16.56408	0.402924	16.56408

$\alpha$ = 23.99

$\beta$1 = -.006

$\beta$2 = -0.47

$\beta$3 = 8.48