# Minitab Instructions for Chapter 9 Technology Exercise

## Correlation Between Exam 1 and Exam 4 (Question 1)

### Entering the Data into Minitab

1. Create two columns, one called exam1 and one called exam4.
2. Enter the data into the two columns

### Summarize the Variables (part a)

You really ought to know how to do this by now.

1. Choose Stat / Basic Statistics / Display Descriptive Statistics
2. Describe exam1 and exam4
3. Click OK

### Scatterplot (part b)

1. Choose Graph / Scatterplot / with Regression
2. The y-variable is exam4 and the x-variable is exam1.
3. Click OK
4. Copy and paste the graph into Word

### Correlation Coefficient and P-value (parts e & f)

1. Choose Stat / Basic Statistics / Correlation
2. Select both exam1 and exam4 for the variables

### Regression Equation (part j)

If you said that you should use the equation given by the computer to make predictions, then do the following. Otherwise the regression equation is that the predicted exam4 value equals the mean of the exam4 variable.

1. Choose Stat / Regression / Regression
2. The response variable is exam4
3. The predictor variable is exam1
4. Click OK
5. The top of this section of output (you may need to scroll up to find it) contains the regression equation. Copy and paste the regression equation into Word.

## Seatbelt Safety (Question 2)

Start a new worksheet for this problem.

1. Label columns as year, seatbelt, and fatality
2. Gather the information for 1985 through 2004 from Figure 1 of the June 2005 Safety Belt Usage in Illinois available from the Illinois Department of Transportation. The data is in a chart, so you'll have to read the percents from the top of the bars. Data is available as late as 2005, but we're only able to get information through 2004 for the next part, so we'll stop in 2004.
3. The National Highway Traffic Safety Administration used to have a wonderful little page with this information available, but they have removed it. From other sources, I have obtained the table below. Use the appropriate years (matched up with the information from step 2) for the fatality rate per 100 million vehicle miles travelled in Illinois.
Year 82 83 84 85 86 87 88 89 90 91 92 93
Rate 2.51 2.27 2.21 2.17 2.15 2.18 2.34 2.15 1.91 1.69 1.58 1.55
Year 94 95 96 97 98 99 00 01 02 03 04 05
Rate 1.68 1.68 1.53 1.41 1.38 1.42 1.38 1.37 1.35 1.36 1.24 N/A

### Making the Fitted Line Plot (part b)

1. Choose Stat / Regression / Fitted Line Plot
2. The response variable is fatality
3. The predictor variable is seatbelt
4. Click OK
5. Copy the graph and paste it into Word

The Fitted Line plot also contains the regression equation and the value of r2, the percent of the variation that can be explained by the regression model. The output in the session window on Minitab gives much of the same information including an ANOVA table that contains the F test statistic and the p-value that can be used for checking correlation.

### Checking for Significant Linear Correlation (parts d & e)

While the p-value can be found from the ANOVA table, it doesn't give the value of r, the correlation coefficient.

1. Choose Stat / Basic Statistics / Correlation
2. The two variables are seatbelt and fatality (order doesn't matter)
3. Click OK

The output gives you the correlation coefficient first and the p-value second. The null hypothesis is that there is no significant linear correlation.

### Give the Regression Equation (part h)

If you determined that there was significant linear correlation (positive or negative) by rejecting the null hypothesis of no significant linear correlation, then you should use the regression equation given by the computer. This was found when you did the fitted line plot. Your equation should look something like "fatality = 3.03814 - 0.0230872 seatbelt" (probably not that exactly).

1. Choose Stat / Regression / Regression
1. The response variable is fatality
2. The predictor variable is seatbelt
3. Click OK
2. The regression equation is given towards the top of the output, you may need to scroll up.

If, however, you decided that there was no signficant linear correlation because you retained the null hypothesis of the correlation test, then you should use the mean of y (y-bar) for the estimated equation. Your equation should be something like "fatality = ####" where #### is the numerical value of the mean of the fatality variable. You'll have to do descriptive statistics to find out what that is.