1) Based on the data shown below, calculate the regression line (each value to two decimal places)

y = x +

1 29.6

2 27.5

3 24.7

4 22.6

5 22.8

6 21.2

7 22

8 17.2

9 19.1

10 16

11 13

12 11

2)A particular professor has noticed that the number of people,P, who complain about his attitude is dependent on the number of cups of coffee,n, he drinks. From eight days of tracking he compiled the following data:

People (P) 11 12 8 8 6 4 4 4

Cups of coffee (n) 1 1 2 3 4 4 5 5

Unless otherwise stated, you can round values to two decimal places.

a) Using regression to find a linear equation forP(n)

P(n)=

b) Find the correlation coefficient

r=

c) Does the correlation coefficient indicate a strong linear trend, a weak linear trend, or no linear trend?

• strong linear trend
• weak linear trend
• no linear trend

d) Interpret the meaning of the slope of your formula in the context of the problem

e) Interpret the meaning of thePintercept in the context of the problem

f) Use your model to predict the number of people that will complain about his attitude if he drinks 10 cups of coffee.

g) Is the answer to part f reasonable? Why or why not?

h) How many cups of coffee should he drink so that no one will complain about his attitude? It is ok to round to one decimal place.

3) 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=ax+b a=-0.953 b=27.4 r2=0.5184 r=-0.72 

Use this to predict the number of situps a person who watches 13 hours of TV can do (to one decimal place)

4) You generate a scatter plot using Excel. You then have Excel plot the trend line and report the equation and ther2 value. The regression equation is reported as

y=38.05x +62.12 and ther2=0.4489.

What is the correlation coefficient for this data set?

r=

5) The line of best fit through a set of data isy=19.871+3.213x

According to this equation, what is the predicted value of the dependent variable when the independent variable has value 80?

y=Round to 1 decimal place.

6) Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as y=49.98x +90.38 and ther=0.463.

What proportion of the variation inycan be explained by the variation in the values ofx?

r =%

Report answer as a percentage accurate to one decimal place.