Kim, a personal trainer, was interested in whether or not there was a linear rel

Question

Kim, a personal trainer, was interested in whether or not there was a linear relationship between the number of visits her clients made to the gym each week and the average amount of time her clients exercised per visit. She took the following data.

Client

1

2

3

4

5

6

Number of visits per week

1

3

4

2

3

5

Average time spent exercising per visit (hours)

2

1.5

1

2

2

0.30

Using the best fit line, estimate the average time spent exercising per visit for 4 visits per week.

2 hours

11.6 hours

10.7 hours

1 hour

Client

1

2

3

4

5

6

Number of visits per week

1

3

4

2

3

5

Average time spent exercising per visit (hours)

2

1.5

1

2

2

0.30

Explanation / Answer

Here to evaluate the best fit line, we will require the values of x,y, xy, x2

Here if fiited line is

y^ = a + bx

then

a =  [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

a = [ 8.8 * 64 - 18 * 22] / [ 6 * 64 - 182]

a = 2.786

b = [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

b = [6 * 22 - 18 * 8.8] / [ 6 * 64 - 182]

b = -0.44

y^ = 2.786 - 0.44x

at x = 4 visits per week

y^ = 2.786 - 0.44 * 4 = 1.03

so 1 hour is the correct answer. Option D is correct.

x y x^2 xy 1 2 1 2 3 1.5 9 4.5 4 1 16 4 2 2 4 4 3 2 9 6 5 0.3 25 1.5 Sum 18 8.8 64 22

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