Question

Reserve Problems Chapter 12 Section 1 Problem 1 During a research, the amount of Internet users was measured. Each time three random groups of 10,000 people of the average age of 20, 40, and 60 were considered. The data are as follows (x1 - the number of years since the beginning of the research, x2 - age, y - number of users): 1800 1550 240 3400 2900 590 4850 4510 1210 6590 6030 1620 X1 1 1 1 3 3 3 5 5 5 7 7 7 X2 20 40 60 20 40 60 20 40 60 20 40 60 (a) Fit a multiple linear regression model using X1 and X2 as the regressors. Round your answers to one decimal place (e.g. 98.7). ỹ = tit X2 (b) Estimate o? Round your answer to the nearest integer (e.g. 9876). (c) Find the standard errors of the regression coefficients. Round your answers to one decimal place (e.g. 98.7). se e(Bo) = ]; se (81) = ); selß2) = (d) Use the model to predict the number of users in random group of 40 years after 4 years of research. Round your answer to the nearest integer (e.g. 9876). Number of users =

Answer 1

Excel > Data > Data Analysis > Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.919112177
R Square	0.844767194
Adjusted R Square	0.810271015
Standard Error	928.4371576
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	2	42218331.67	21109165.83	24.48871772	0.000228784
Residual	9	7757960	861995.5556
Total	11	49976291.67
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	3810.5	855.976765	4.451639526	0.001596411	1874.14603	5746.85397	1874.14603	5746.85397
X1	593.8333333	119.8607216	4.954361405	0.000786581	322.6895433	864.9771233	322.6895433	864.9771233
X2	-81.125	16.41260525	-4.942847206	0.000799109	-118.2528925	-43.99710747	-118.2528925	-43.99710747

a)

Regression equation:

Y^ = 3810.5+593.8*X1-81.1*X2

b)

Estimate (σ^2) = MSE = 861996

c)

	Standard Error
Intercept(β0)	856.0
X1(β1)	119.9
X2(β2)	16.4

d)

If X1 = 4 and X2 = 40

Y^ = 3810.5+593.8*X1-81.1*X2

Y^ = 3810.5+593.8*4-81.1*40 = 2941.7

Number of users = 2942 (rounded)