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): у 1400 1150 160 3000 2500 510 4450 4110 810 6190 5630 1220 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 Xi and X2 as the regressors. Round your answers to one decimal place (e.g. 98.7). û Jx1+! Jxz (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(Bo) = se(B.) ; se se(B2) (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

using excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.908247
R Square	0.824912
Adjusted R Square	0.786003
Standard Error	955.3398
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	2	38699825	19349913	21.20134	0.000393
Residual	9	8214067	912674.1
Total	11	46913892
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	3389.167	880.7797	3.847916	0.003919	1396.704	5381.629
x1	572.5	123.3338	4.641873	0.001216	293.4995	851.5005
x2	-77.125	16.88818	-4.5668	0.001353	-115.329	-38.9213

Ans a )the regression equation is

$\hat{y} = 3389.2+572.5x_1-77.1x_2$

b )

$\hat{\sigma}^2$ = 955.3398² = 912674.1 ~912674

c ) $Se(\beta_0)$ =880.8

$Se(\beta_1)$=123.3

$Se(\beta_2)$=16.9

d ) for x1 = 4 . x2 = 40

$\hat{y} = 3389.2+572.5*4-77.1*40$

$\hat{y} =2595.2\approx 2595$