Question

 

Suppose a researcher thinks that there is a relationship between how much a person works out and the amount of time they spend watching TV. The research collects data on a sample of 5 people, finding out the number of workouts they participate in a month and the number of hours of TV they watch each week. The data are listed below:

Participant # of workouts (X) # of tv hours (Y)

1 18 3

2 11 1

3 3 10

4 6 14

5 10 2

a. Calculate the relationship between number of workouts and hours of television viewing for the participants. (3 points)

 

b. Using the data you have available to you, get the regression equation for predicting number of hours of TV watched from the number of workouts. Include whatever numerical values you can in your equation. (3 points)

 

c. Use the regression equation from above to predict the number of hours of TV watched for a person who works out 4 times per month. (2 points)

Answer 1

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a) A negative correlation exist. Correlation is -0.6867 . Detailed step is given below..

b) Regression equation is ŷ = -0.68885X + 12.613. Possible values of X are 0,1,2, ..., 18. Because when 19 times work out per month result in negative number of hours tv watched which is not possible. So upto 18 times workout per month is possible. THAT IS x can takes values only upto 18. Detailed steps to obtain regression is given below.

c) put x = 4 in regression equation , i.e,

ŷ = -0.68885*4 + 12.613 = 9.8576

Approximately 10 hours