Statdisk Notes for Activity 9

Creating the Worksheet

The worksheet will be provided to you by the instructor in Minitab format and on the website. That is so that you won't know whose blood pressure and pulse rate is whose. Although gender and age may be related to blood pressure and pulse rate, we're not collecting that information for this project. If this were a more clinical study, we would collect and analyze that data and more.

If you're using Statdisk, you may need to type in the information (you might be able to copy and paste from the website).

The variables recorded are called systolic, diastolic, and pulse.

  1. Enter the data for your x (predictor) variable into column 1
  2. Enter the data for your y (response) variable into column 2
  3. Click at the top of the columns where the 1 and 2 are and supply the names of the variables.

This example uses the predictor variable x = systolic and the response variable y = diastolic but you should use your assigned variables.

Should you wish to duplicate the results in the example, the data is from the Spring 2005 semester of Math 113.

Generate a Scatterplot (Question 3)

Scatterplot of diastolic pressure vs systolic pressureThis question wants you to generate a scatterplot and try to determine the value of the correlation coefficient based on the scatterplot alone.

  1. Choose Data / Scatterplot
  2. Click Plot

Now make a guess as to what you think the correlation coefficient would be. For my data, there appears to be a very slight positive correlation, but it's not very good at all. I would guess about r = 0.1 (later we'll find out I'm not very close, but this is just a guess).

Summarizing the Data (Question 4)

  1. Choose Data / Descriptive Statistics
  2. Choose Column 1 for the predictor (x) variable
  3. Click Evaluate
  4. Repeat this process with Column 2 for the response (y) variable

Copy the sample size, mean, standard deviation, and variance onto your activity sheet.

Finding Correlation (Questions 5&6)

Correlation and regression resultsCorrelation and Regression are combined into one screen on Statdisk, so you'll be using these results for several questions.

  1. Choose Analysis / Correlation and Regression
  2. Choose column 1 for the x variable and column 2 for the y variable.
  3. Click Evaluate

The top of the output contains the Correlation Results. You need the Correlation coefficient, r, and the p-value.

For question 6, repeat these steps, but switch the x and y variables in step 2.

Switch the x and y back to columns 1 and 2 before you proceed with the rest of this activity. The rest of the questions assume the original order, not the switched order for question 6.

Regression (Question 7)

If you are looking at the output used for question 6, be sure to switch the order of the variables back to the proper order before continuing.

  1. Choose Analysis / Correlation and Regression
  2. Choose column 1 for the x variable and column 2 for the y variable.
  3. Click Evaluate

Look at the section that is labeled Regression Results

The regression equation is Y = b0 + b1x but DO NOT write that on your paper. Replace the y intercept b0 and the slope b1 by the values given that follow. Replace the y and the x by the names of the variables (x = systolic and y = diastolic in my example)

Don't write: Y = b0 + b1x
Do write: diastolic = 42.92439 + 0.2244902 systolic

ANOVA table (Question 8)

Statdisk does NOT give the Analysis of Variance table directly. It does give some of the information from the table, you just have to match things up and calculate some by hand or use Minitab in the first place.

This table will tell you how to find the values in Statdisk and fill them in to the ANOVA table. The labels in the inside of the table correspond to the labels from the Correlation and Regression output shown above from question 5.

Source SS (variation) DF MS (variance) F P
Regression (explained) Explained Variation 1 see below see below see below
Residual (unexplained) Unexplained Variation Degrees of Freedom (top) see below blank blank
Total Total Variation Sample size - 1 see below blank blank

Finding the Variances (MS column)

The MS (variance) column is found by dividing the SS (variation) column by the DF column. You'll need to do this by hand, Statdisk doesn't give you the values there (at least not directly). Do this for each row of the table.

Finding the F Test Statistic

There is only one number in the F column, that's in the Regression row. The F test statistic is the MS(Regression) divided by the MS(Residual).

Finding the p-value

Finding the p-value for an F distribution results in StatdiskTo find the p-value, which is what the P stands for, using Statdisk you'll need to follow these steps.

  1. Choose Analysis / Probability Distributions / F Distribution
  2. The numerator degrees of freedom are the degrees of freedom for the Regression row, which are always 1 for simple regression.
  3. The denominator degrees of freedom are the degrees of freedom for the Residual row, which is n-2, given as the "degrees of freedom" at the top of the Statdisk output.
  4. The F-value is the F test statistic
  5. Leave the area to the right of the F value blank
  6. Click evaluate

The F test is a right tail test, so the cumulative probability to the right of the test statistic F is the p-value.

Completed ANOVA table

Taking all the information supplied above, here is what the completed ANOVA table would look like for the data I used to prepare these instructions.

Source SS (variation) DF MS (variance) F P
Regression (explained) 293.3419 1 293.3419 6.650714 0.014275
Residual (unexplained) 1543.739 35 44.10683    
Total 1837.081 36 51.03003    

Use the explanation on your activity sheet about the ANOVA table to answer questions 10 and 11.