# Correlation and Regression

May 20th, 2013
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Question description

Consider the following data that compares the Consumer Price Index (CPI) with subway fare in a particular city:

CPI 30.2 48.3 112.3 162.2 191.9 197.8

Subway Fare 0.15 0.35 1.00 1.35 1.50 2.00

a. Using the given data, construct a scatter plot with CPI as the independent variable (x) and subway fare as the dependent variable (y).

b. Write the regression equation that predicts subway fare in terms of CPI.

c. Using the equation found in Part b, find the best predicted cost of subway fare when the CPI is 182.5.

1. Listed below are baseball team statistics consisting of the proportions of wins and the result of this difference:

Difference (number of runs scored) – (number of runs allowed). The statistics are from a recent year, and the

teams are NY—Yankees, Toronto, Boston, Cleveland, Texas, Houston, San Francisco, and Kansas City.

Difference 163 55 –5 88 51 16 –214

Wins 0.599 0.537 0.531 0.481 0.494 0.506 0.383

a. Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of

r from Table A–6 using α = 0.05.

b. Is there sufficient evidence to conclude that there is a linear correlation between the proportion of wins

and the above difference?

2. One classic application of correlation involves the association between the temperature and the number of

times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 min and the corresponding

temperatures in °F:

Chirps in 1

min

882 1188 1104 864 1200 1032 960 900

Temperature (°F)

69.7 93.3 84.3 76.3 88.6 82.6 71.6 79.6

a. Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of

r from Table A–6 using α = 0.05.

b. Is there a linear correlation between the number of chirps in 1 min and the temperature?

Below is a control chart for the temperature of a freezer unit in a restaurant. The owner of the restaurant is

deciding whether or not to buy a new unit. The two charts display the temperature for the past two weeks.

Write a paragraph analyzing the control charts and argue whether the owner should buy a new unit or not.

Control Charts for Variation and Mean

3. Below is a control chart for the temperature of a freezer unit in a restaurant. The owner of the restaurant is deciding whether or not to buy a new unit. The two charts display the temperature for the past two weeks. Write a paragraph analyzing the control charts and argue whether the owner should buy a new unit or not. (5-6 sentences) See Graph attachment.

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