Suppose you are determining the association between the weight of a car and the miles per gallon that the car gets. Answer the following questions:
1. In your own words, define correlation and talk about how you can use correlation to determine the relationship between these two variables.
2. Before you look at some data, what kind of association do you think will exist between the weight of a car and the miles per gallon that the car gets? Will it be positive or negative?
3. Given the data below, use Excel or other technology to calculate the correlation coefficient for this data:
Model 
City MPG 
Weight 
Mazda MX5 Miata 
25 
2365 
Mercedes/Benz SLK 
22 
3020 
Mitsubishi Eclipse 
23 
3235 
Pontiac Firebird 
18 
3545 
Porsche Boxster 
19 
2905 
Saturn SC 
27 
2420 
4. Now that you have calculated the correlation, what does this value represent? What does it tell you about the relationship between these two variables?
Examples
Example 1: Safety experts are trying to determine how long it takes a specific brand of car to come to a complete stop. They have determined that the speed of the car has a large impact on how long it takes to come to a complete stop. They decide to gather data by having the car go 10, 30, 50, 70 and 90 miles per hour and then determine how many feet it takes to come to a complete stop at each of these speeds.
Example 2: Drama students at a large university recently put on a production of Phantom of the Opera. Some students jokingly said that only the female students went to see the play, and one of the students wanted to see if a higher proportion of female students had seen the play than males. To gather data, the student went around campus randomly selecting students and asking them their gender and if they went to see the production.
Complete the following for both Example 1 and Example 2:
5. State the explanatory and response variables in each example, and state what type for each of the variables.
6. For each example, discuss an appropriate analysis or procedure to use to determine if there is an association between the two variables.
7. Given the following data where city MPG is the response variable and weight is the explanatory variable, explain why a regression line would be appropriate to analyze the relationship between these variables:
Model 
City MPG 
Weight 
Mazda MX5 Miata 
25 
2365 
Mercedes/Benz SLK 
22 
3020 
Mitsubishi Eclipse 
23 
3235 
Pontiac Firebird 
18 
3545 
Porsche Boxster 
19 
2905 
Saturn SC 
27 
2420 
8. Construct the regression line for this data.
9. Interpret the meaning of the yintercept and the slope within this scenario.
10. What would you predict the city MPG to be for a car that weighs 3000 pounds?
11. If a car that weighs 3000 pounds actually gets 32 MPG, would this be unusual? Calculate the residual and talk about what that value represents.

College Graduate 
Not a College Graduate 
Total 
Male 
56 
32 
88 
Female 
62 
41 
103 
Total 
118 
73 
191 
Answer the following question:
12. Have the assumptions for this test been met? Why or why not?
13. State the null and alternative hypothesis for this test.
14. Calculate the test statistic for this test. Explain what this test statistic represents.
15. Use technology, like Excel, to calculate the pvalue for this test. Explain what this pvalue represents.
16. State the conclusion for this test at the 0.05 level of significance. Do you think these variables are dependent/associated? Why or why not?
17. Describe the relationship between two variables that have a correlation coefficient value:
a. Near 1
b. Near 0
c. Near 1
18.Data was collected where a weightlifter was asked to do as 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 yintercept and the slope within this scenario.
c. Calculate r^{2} 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.
19.Given the linear regression equation:
y = 1.6 + 3.5x_{1} – 7.9x_{2} + 2.0x_{3}
a. Which variable is the response variable? How many explanatory variables are there?
b. If x_{1} = 2, x_{2} = 1 and x_{3} = 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 x_{1} is 0.419. Construct a 90% confidence interval for the coefficient of x_{1}.
d. Using the information from part (c) and 5% level of significance, test the claim that the coefficient of x_{1} is different from 0. What does your conclusion mean in relation to x_{1} predicting y?
20.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 
902 
Test whether gender and type of favorite movie are independent at the .05 level of significance. Show all five steps of this test.
21.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.
Subject  Mathematics 
Due By (Pacific Time)  11/01/2015 12:00 am 
Tutor  Rating 

pallavi Chat Now! 
out of 1971 reviews More.. 
amosmm Chat Now! 
out of 766 reviews More.. 
PhyzKyd Chat Now! 
out of 1164 reviews More.. 
rajdeep77 Chat Now! 
out of 721 reviews More.. 
sctys Chat Now! 
out of 1600 reviews More.. 
sharadgreen Chat Now! 
out of 770 reviews More.. 
topnotcher Chat Now! 
out of 766 reviews More.. 
XXXIAO Chat Now! 
out of 680 reviews More.. 