JMP Assignment 4

Correlation and Regression

Regression of Brainsize and IQ

We will investigate the relationship of brain size, as determined by MRI scans, on IQ scores. The dataset we will use is called brainsize.jmp and is available here as well as on the Mac server.

First we will look at the relationship between the Full Scale IQ score (FSIQ) and brainsize (MRI_Count).

1. Open the brainsize.jmp dataset

2. Analyze -> Fit Y by X and add MRI_Count to the X list and FSIQ to the Y list. Click OK.

3. Click on the box labeled Fitting below the scatterplot. Click on Fit Line so it is checked. The least squares fit line will appear in the scatterplot and the results of the statistical analysis will appear at the bottom of the output.

Question 1: Print and hand in the resulting JMP output. What is the y-intercept of the model? What is the slope?

Question 2: Is the slope significantly different from 0? What is the p-value? Does brainsize seem to be related to IQ?

Question 3: What is the R² value from this model? Explain what an R² value measures. What is the largest and smallest values R² can possibly be? Does brainsize explain IQ very well?

Question 4: What value of FSIQ does the model predict for a subject with an MRI_Count of 900,000?

Regression of Height and IQ

Now use the methods I showed you above to examine if a persons height (Height) is a good predictor of IQ (FSIQ).

Question 5: Is the slope of this model significantly different from zero? What is the p-value? Does height seem to be related to a persons IQ?

Question 6: What is the R² value for this model? Is height a good predictor of IQ?

Correlations of IQ scores

Next we will investigate the correlations between the 3 IQ scores: Full Scale IQ scores (FSIQ), Verbal IQ scores (VIQ) and Picture IQ scores (PIQ).

1. Analyze -> Correlation of Y's. Click on FSIQ and then on >> Add >>. Repeat for VIQ and PIQ. Click on OK.

2. On the bottom of the window that comes up are three small symbols: a checkmark, a dollar sign and an asterisk. Click on the checkmark and then Scatterplot Matrix. The window should now show correlation coefficients on the top of the screen and scatterplots on the bottom.

Question 7: Print and hand in the JMP output. What is the correlation coefficient between FSIQ and VIQ? What is the correlation coefficient of FSIQ and PIQ?

Question 8: Which pair of IQ coefficients have the lowest correlation coefficient?

Correlation of Tobacco and Alcohol Use

Finally we will investigate data from a British government survey of household spending to examine the relationship between household spending on tobacco products and alcoholic beverages. The dataset vices.jmp (available here and on the Macintosh server) contains average weekly household spending, in British pounds, on tobacco products (Tobacco) and alcoholic beverages (Alcohol) for each of the 11 regions of Great Britain (Region).

Question 9: Repeat the above procedures to get a correlation coefficient and scattergram of Tobacco and Alcohol. Print and hand in the JMP output. What is the correlation coefficient between Tobacco and Alcohol?

The relationship between Tobacco and Alcohol looks linear with the exception of one outlier. The outlier is Northern Ireland which is the last observation in the dataset. On the data spreadsheet click on the far left of Northern Irelands row of data (in the cell with the number 11) to highlight that cell. Then click on Rows -> Exclude/Include. A symbol will appear in that far left cell that indicates that this row will be excluded from further analyses.

Question 10: (10 points) Use JMP to make a scattergram of Tobacco and Alcohol excluding the Northern Ireland data. Print and hand in the JMP output. What is the new correlation coefficient for this relationship?

E-mail Mr. Callahan at stat110@edcallahan.com with questions or comments about this web site or about the class itself.