Question

In the following study a researcher was interested in whether infant mortality was related to the level of pollution in the city. For this purpose he collected the following data for n = 20 heavily populated localities. For each locality, an index (X) measuring the average daily level of pollution was determined along with the average infant mortality rate, (Y) over the past ten years. The data is tabulated below: 2. Locality (i) Pollution Index (X) Infant Mortality Rate 3.32 2.41 KY) Locality (i) Pollution Index (X) Infant Mortality Rate 5.09 4.84 KY) 6. 9. 10 3 5 4 23.6 21.9 23.2 | 12.7 | 14.8 26.3 17.8 27.2 17.5 6.4 3.85 5.59 5.8 4.65 5.98 5.75 3.17 2.68 19 20 18 17 13 14 15 16 11 12 23.9 18.9 | 20.1 18.4 2.73 5.74 4.16 | 4.96 18.6 28.2 21.3 18.7 18.3 24 5.22 4.74 4.44 6.61 Estimate the parameters of the least squares line. Determine 95% confidence limits for the parameters of the least squares line. Plot a graph of the data showing the least squares line. What conclusions would you make from this analysis? Predict the infant mortality rate in the city where the pollution index was 10.7. Compute 95 % prediction limits for this mortality rate. A. B. C. D. E.

Answer 1

Answer:

a).

The estimated regression line is

y = 1.2405+0.1666*x

b).

95% CI for intercept = (-0.482, 2.963)

95% CI for slope= (0.083, 0.250).

c).

y = 0.167x+1.240 RP = 0.496 } + + + + + + + + + + + + + + + + + + + 51015 + + + + + + + 2025 30

d).

To test the significance of the model, calculated F=17.69, P=0.0005 which is < 0.05 level of significance. Ho is rejected. The linear relation is significant.

e).

when pollution index is 10.7,

predicted y value is = 3.0226

95% prediction interval for this mortality rate is (0.9538 , 5.0914 )

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis

Regression Analysis
	r²	0.4957	n	20
	r	0.7041	k	1
	Std. Error of Estimate	0.8898	Dep. Var.	y
Regression output						confidence interval
variables		coefficients	std. error	t (df=18)	p-value	95% lower	95% upper
Intercept	a =	1.2405	0.820	1.513	.1477	-0.482	2.963
x	b =	0.1666	0.040	4.206	.0005	0.083	0.250
ANOVA table
Source	SS	df	MS	F	p-value
Regression	14.009	1	14.009	17.69	.0005
Residual	14.252	18	0.792
Total	28.261	19
Predicted values for: y
		95% Confidence Interval		95% Prediction Interval
x	Predicted	lower	upper	lower	upper	Leverage
10.7	3.0226	2.1366	3.9085	0.9538	5.0914	0.225