Question

Reserve Problems Chapter 12 Section 1 Problem During a research, the amount of Internet users was measured. Each time three random groups of 30,000 people of the average age of 20, 40, and 60 were considered. The data are as follows xj - the number of years since the beginning of the research, 2 - age. y number of users): 1700 3450 220 2300 2800 570 4750 1420 110 490 5920 2520 7 12 20 40 20 40 60 20 40 60 20 40 60 (A) re a multiple linear regression model using and as the regressors Round your answers to the decimal place (e.g. 98.7), 9 () Estimated Round your answer to the nearest Integer (eg:9876). (c) Find the standard errors of the regression coeficients Round your answers to one decimal place (-0.987), Isel) - (a) 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 eger .. 9976), Number of users -

Answer 1

Solution

we will solve it by using excel and the steps are

Enter the Data into excel

Click on Data tab

Click on Data Analysis

Select Regression

Select input Y Range as Range of dependent variable.

Select Input X Range as Range of independent variable

click on labels if your selecting data with labels

click on ok.

So this is the output of Regression in Excel.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9
R Square	0.8
Adjusted R Square	0.8
Standard Error	934.2
Observations	12.0
ANOVA
	df	SS	MS	F	Significance F
Regression	2.0	41323985.0	20661992.5	23.7	0.0
Residual	9.0	7854706.7	872745.2
Total	11.0	49178691.7
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	3705.2	861.3	4.3	0.0	1756.8	5653.6	1756.8	5653.6
x1	588.5	120.6	4.9	0.0	315.7	861.3	315.7	861.3
x2	-80.1	16.5	-4.9	0.0	-117.5	-42.8	-117.5	-42.8

a) From above output we can write

y = 3705.2+588.5*x1- 80.1*x2

b) $\sigma ^{2}$ = MS Residual =  872745.2

c)

	Coefficients	Standard Error
Intercept	3705.2	861.3
x1	588.5	120.6
x2	-80.1	16.5

d)

Predict number of users when x1= 4, x2= 40

y = 3705.2+588.5*x1- 80.1*x2

y = 3705.2+588.5*4- 80.1*40

y = 2855

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