Use Minitab R, or your preferred software for this question, but calculate the 9

Question

Use Minitab R, or your preferred software for this question, but calculate the 90% confidence interval for the coefficient for cable by hand but use the SE from the software output and do the test whether age and number of TVs should be dropped by hand (use ANVOA table to get p-value and confirm with software). The data in the table below contains observations on age sex male = O female = 1 number of television sets in the household, cable no = 0 yes = 1 and number of hours of tele ision watched per week. Using hours of television watched per week as the response, you can use Minitab s Regress or R's In, command e g model?lm hours age+ sex+num v+ cable to fit a least squares regression model to all the other given variables 22,22,50,43,54,24,15,23,34,18,58,19,25,15,21,30,37,44,29,27,30,17,15,21,47,26,13,39,22,20,14,47,21,38,23,32,19,15,21,18 Age: Sex: Num. TV: 2,2,1,1,1,1,2,1,1,1,2,1,1,1,1,2,2,2,1,1,2,1,2,1,1,1,2,2,1,1,1,1,1,1,2,1,2,1,1,2 Cable: 1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0,0,1 Hours TV:28,16,18,20,25,14,21,7,12,14,15,12,10,11,12,18,17,20,21,15,17,18,13,21,23,11,10,21,13,12,10,19,12,21,8,16,13,9,11,21 What is the estimated value of the regression coefficient for age? 0.1000 2 pt(s)] are correct. r receipt no. is 155-6853Previous Tries What is the estimated value of the regression coefficient for cable? 4.1980 [2 pt[s)] are correct. r receipt no. is 155-9860 According to the regression equation, which of the following statements is true? Incorrect From the data given, one can not tell which gender watches more television per week. Incorrect Femalcs watch tekkvision 3.577 hours more per weck than males Incorrect Females watch television approximately the same number of hours per week as males Correct: Males watch television 3.577 hour s more per week than females. ? re correct. r recelpt no. is 155-5301 What is the value of the test-statistic for the overall regression signifikance test? 12.6200 (3 pts)) ou are correct. r receipt no, is 155-893 What are the degrees of treedom associatod with the test-statistic? Numcrator:4 Denominator: 35 [1 pt(s)) ou are correct. r receipt no. is 155-4574Previous Tries Select the interval below that contains the p-value for this test. Correct: p-value S 0.00 Incorrect 0.001

Explanation / Answer

ANS : By using R software we get,

a=read.csv("C:/Users/dciuser/Desktop/Book1.csv",header = TRUE);a
model=lm(a$hours.tv~.,data=a);summary(model)

Output:

Call:

lm(formula = a$hours.tv ~ ., data = a)

Residuals:

Min 1Q Median 3Q Max

-8.3823 -2.3661 0.4466 1.9826 8.2178

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) 11.66563 2.30807 5.054 1.36e-05 ***

age 0.10000 0.05001 2.000 0.05333 .  

sex -3.57660 1.11828 -3.198 0.00293 **

num.tv 0.85899 1.14453 0.751 0.45796   

cables 4.19849 1.21864 3.445 0.00150 **

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.364 on 35 degrees of freedom

Multiple R-squared: 0.5905, Adjusted R-squared: 0.5437

F-statistic: 12.62 on 4 and 35 DF, p-value: 1.854e-06

For ANOVA :

anova(model)
Analysis of Variance Table

Response: a$hours.tv
Df Sum Sq Mean Sq F value Pr(>F)   
age 1 223.72 223.716 19.7676 8.439e-05 ***
sex 1 196.51 196.506 17.3633 0.0001921 ***
num.tv 1 16.72 16.717 1.4771 0.2323592   
cables 1 134.33 134.331 11.8695 0.0014995 **
Residuals 35 396.11 11.317   

For confidence interval

confint(model,level=0.90)
5 % 95 %
(Intercept) 7.76598371 15.5652751
age 0.01551238 0.1844932
sex -5.46602111 -1.6871746
num.tv -1.07477542 2.7927612
cables 2.13950085 6.2574726

Gives 90% C.I. for all the variables.

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