1.Describe the relationship between two variables that have a correlation coefficient value:

a.Near -1

b.Near 0

c.Near 1

2.Data was collected where a weightlifter was asked to do many repetitions as possible using different amounts of weight. Below is a table that shows how much weight was on the bar, and how many repetitions the weightlifter could do:

Weight

200

300

400

500

Reps

42

27

12

3

a.Calculate the correlation for this data. What does this value tell you about the relationship between these two variables?

b.Determine the least squares regression line for this data. Interpret the values for the y-intercept and the slope within this scenario.

c.Calculate r² for this data and describe what it represents.

d.Using the regression line from part (b), calculate the predicted number of repetitions for this weight lifter if the weight is 400 pounds, and then calculate and interpret the residual for that weight using the data.

3.Given the linear regression equation:

y = 1.6 + 3.5x₁ - 7.9x₂ + 2.0x₃

a.Which variable is the response variable? How many explanatory variables are there?

b.If x₁ = 2, x₂ = 1 and x₃ = 5, what is the predicted value for y?

c.Supposed the n = 12 data points were used to construct the given regression equation above, and that the standard error for the coefficient x₁ is 0.419. Construct a 90% confidence interval for the coefficient of x₁.

d.Using the information from part (c) and 5% level of significance, test the claim that the coefficient of x₁ is different from 0. What does your conclusion mean in relation to x₁ predicting y?

4.Suppose a researcher is analyzing the relationship between gender and favorite type of movie out of drama, science fiction and comedy. Here is the data using a random sample:

Drama

Science Fiction

Comedy

Total

Male

28

152

218

398

Female

213

102

189

504

Total

241

254

407

710

Test whether gender and type of favorite movie are independent at the .05 level of significance. Show all five steps of this test.

5.Suppose you wanted to test whether M&M's made the same amount of each color. You could run a goodness of fit test to see if each color had the same proportion. Suppose you took a sample of M&M's and below is the breakdown by color:

Color

OBSERVED Counts

Blue

15

Orange

14

Green

10

Yellow

11

Red

4

Brown

6

Total

60

Test whether each color has the same proportion. Show all five steps of this test at the 10% level of significance.