Question

A regression analysis was performed to determine if there is a relationship between hours of TV watched per day (x) and number of sit ups a person can do (y ). The results of the regression were: y=ax+b a=-1.326 b=30.621 p2=0.6561 r=-0.81 Use this to predict the number of sit ups a person who watches 14 hours of TV can do, and please round your answer to a whole number.

use second picture please

Answer 1

1.

Regression equation of y on x is given by

ឬ = 1,326 + 30.621

For , predicted number of sit ups is given by

T = 14

y = -1.326 * 14+ 30.621 = 12.057 12

2.

Suppose, random variables X and Y denote scores in first and second quiz respectively.

Regression equation of y on x is given by

y- y = byz (1 - 2

Here,

Number of pairs of observation

8=U

1 J = Συ; = Σ9 = 20.625- Σ η 8 =1 i=1

= 23.25 =1

Cou(X,Y) Var(X) = 1.037084

:.y - 20.625 = 1.037084 (1 – 23.25)

y - 20.625 = 1.0370842 1.037084 * 23.25

y = 1.0370843 + 20.625 - 24.1122

$\tiny \therefore y=1.037084x-3.4872$

Scatter plot with line that best fits the data is as follows.

Scatter plot and line of best fit 28 26 T 24 T 22 > 20 o 18 16 0 14 o 18 20 22 24 26 28 30 X

For , predicted score in second quiz is given by

= 16

$\tiny \hat y=1.037084*16-3.4872=13.10614\approx 13$