Question

QUESTION A: A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).

The results of the regression were:

y=a+bx
a=26.695
b=-0.65
r2=0.531441
r=-0.729

Assume the correlation is significant (p-value < α), and use this to predict the number of situps a person who watches 13.5 hours of TV can do (to one decimal place)

QUESTION PART B: Run a regression analysis on the following bivariate set of data with y as the response variable.

x	y
19.2	75.4
32.3	52.5
17.7	68.7
22.6	65.6
12.9	74.2
25.2	55.9
18.8	66.9
19.6	68.3
19.1	74.8
16.7	73.7
21.8	64.6
22.9	69.5

Find the correlation coefficient and report it accurate to three decimal places.
r =

What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5%...you would enter 84.5 without the percent symbol.)
r² = %

Based on the data, calculate the regression line (each value to three decimal places)

ˆy=  +  x

Predict what value (on average) for the response variable will be obtained from a value of 20 as the explanatory variable. Use a significance level of α=0.05 to assess the strength of the linear correlation.

What is the predicted response value? (Report answer accurate to one decimal place.)
ˆy=

Answer 1

A)

predicted number of situps =26.695-0.65*13.5 =17.92

B)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

-0.859

proportion of the variation in y can be explained by the variation in the values of x r²=73.7 %

y^ =94.033+(-1.279)*x

predicted response value =94.033-1.279*20 =68.5 (please try 68.4 if this comes incorrect)