Question

Using the data in the Excel file under the tab Problem1, develop a regression equation for a country’s lung cancer death rate based on cigarette consumption.

1. Is this a good regression model?  Why or why not?

2. If Cigarette Consumption was 725, what would you predict the Lung Cancer Death Rate to be?

3. Using your regression model, what is the Residual Value for Finland?

4. Do you think there are any outliers in the model?  If so, what would you do with them?

Country	Cigarette Consumption	Lung Cancer Death Rate
Austria	455	170
Canada	510	150
Denmark	380	165
Finland	1115	350
Great Britain	1145	465
Holland	460	245
Iceland	220	58
Norway	250	90
Sweden	310	115
Switzerland	530	250
USA	1280	190

Answer 1

All the calculation is done in MS EXCEL and the analysis is shown below.

a.

Here the coefficient of determination or the square to the correlation coefficient is 0.549 i.e. only 54.9% variability of the total variability is explained by the model. Hence the model is moderately good.

b.

Here, the regression model is,

Lung cancer death rate(y)=65.75+0.23*Cigarette consumption(x)

So, we replace x=725 and get the lung cancer death rate.

For 725 consumption of cigarettes, the death rate due to lung cancer is=232.5

c.

Using the model the residual value for Finland is=328.08

d.

Here in this given data, there is no outlier from the analysis shown below.

Country	Cigarette Consumption	Lung Cancer Death Rate					SUMMARY OUTPUT
Austria	455	170		345	Q1
Canada	510	150		822.5	Q3		Regression Statistics
Denmark	380	165		477.5	IQR		Multiple R	0.740972337
Finland	1115	350					R Square	0.549040004
Great Britain	1145	465		-371.25	LOWER BOUND		Adjusted R Square	0.498933338
Holland	460	245					Standard Error	84.12962829
Iceland	220	58					Observations	11
Norway	250	90		1538.75	UPPER BOUND
Sweden	310	115					ANOVA
Switzerland	530	250						df	SS	MS	F	Significance F
USA	1280	190					Regression	1	77554.39625	77554.39625	10.95742	0.009081
							Residual	9	63700.1492	7077.794356
							Total	10	141254.5455
								Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
232.5		death rate				Intercept	65.74885702	48.95871046	1.342945033	0.212173	-45.0034	176.5012	-45.0034	176.5012
							Cigarette Consumption	0.229115338	0.069214952	3.310200048	0.009081	0.07254	0.38569	0.07254	0.38569
							RESIDUAL OUTPUT				PROBABILITY OUTPUT
							Observation	Predicted Lung Cancer Death Rate	Residuals	Standard Residuals		Percentile	Lung Cancer Death Rate
							1	169.9963357	0.0036643	4.59114E-05		4.545455	58
							2	182.5976793	-32.59767928	-0.408428893		13.63636	90
							3	152.8126854	12.18731463	0.152699564		22.72727	115
							4	321.2124586	28.78754138	0.360690207		31.81818	150
							5	328.0859188	136.9140812	1.715449318		40.90909	165
							6	171.1419124	73.85808761	0.92539646		50	170
							7	116.1542313	-58.15423133	-0.728636789		59.09091	190
							8	123.0276915	-33.02769146	-0.413816682		68.18182	245
							9	136.7746117	-21.77461173	-0.272822507		77.27273	250
							10	187.179986	62.82001397	0.787096179		86.36364	350
							11	359.0164893	-169.0164893	-2.117672768		95.45455	465
								#NAME?