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

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 (but use the ANVOA tables from software).

The data in the table below contains observations on age, sex (male = 0, female = 1), number of television sets in the household, cable (no = 0, yes = 1), and number of hours of television watched per week. Using hours of television watched per week as the response, you can use Minitab's Regress or R's lm() command [e.g., model <- lm(hours~age+sex+num.tv+cable)] to fit a least squares regression model to all the other given variables.

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

question:

1.Select the interval below that contains the p-value for this test.
p-value 0.001
0.001 < p-value 0.01
0.01 < p-value 0.05
0.05 < p-value 0.1
0.1 < p-value 0.25
p-value > 0.25

2. Test whether age and number of TV sets are needed in the model or should be dropped. What is the value of the test-statistic?

3. What are the degrees of freedom associated with this test? Numerator:  Denominator:

4. Select the interval below that contains the p-value for this test.
p-value 0.001
0.001 < p-value 0.01
0.01 < p-value 0.05
0.05 < p-value 0.1
0.1 < p-value 0.25
p-value > 0.25

Age: 22,22,50,43,54,24,15,23,34,18,58,19,26,15,21,30,37,44,29,27,30,17,15,21,47,26,13,39,22,20,14,47,21,38,23,32,19,15,21,18 Sex: 0,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,1,1,0,1,0 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

Explanation / Answer

1) p-value 0.001

from above test statistic and df values(35,4,13.08784) . if we calculate the p value . we will get p is less than 0.001

  

2)

t Stat P-value

age 2.203184513 0.034256 since p-value is less than alpha (0.05), its coefficient value is significant and I conclude that it shouldn’t be dropped.

tv sets 0.738339436 0.465231 since p-value is greater than alpha (0.05), its coefficient value is NOT significant and I conclude that it should be dropped.

3)Numerator: 3 Denominator: 36

4)p-value 0.001

from above test statistic values and df values(3,36,2.203184513) .if we calculate the p values we will get p is less than 0.001

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