STAT 462 Feb. 23 LAB
Activity 1: Use the dataset trees.txt at www.stat.psu.edu/~rho/462data/ . Copy and paste the
data to a Minitab worksheet. For a sample of black cherry trees, the data are Y = estimated
volume of wood in tree, X1 = diameter of tree, and X2 = height of tree.
a. Determine the correlation between Diameter and Height (the two x-variables).
(Stat>Basic Stats>Correlation)
Correlation =
b. Determine the regression equation for predicting Y = volume using X2 = Height.
Write the estimated equation -
What is the value of SSR(Height), the regression SS for this regression?
c. Determine the regression equation for predicting Y (volume) using X1 = diameter and X2 =
height. In the regression dialog box, list the predictors in the order Diameter Height.
Write the estimated equation -
What is the value of SSR(Height|Diameter)?
d. Compare the coefficient multiplying height in the models determined in parts a and b.
Specifically, are they equal?
e. Compare the values of SSR(Height) and SSR(Height|Diameter). Are they equal?
f. Use both predictors to predict Y = volume. Store the residuals and fits. Then, plot residuals
versus fits. When creating the plot, in the Data Display section enter Lowess as the second item
and Graph in the corresponding “For Each” box. This will put a rough estimate of the pattern onto
the plot. What pattern is indicated? What action should we take?
g. Create a column that contains Diameter-squared. Then, use column as a predictor along with
height and diameter to predict volume. What are the indications that this is a better model than
one that does not include diameter-squared?
Activity 2. Use the dataset brandpref.txt linked at www.stat.psu.edu/~rho/462data/. Y = rating
of a pastry product. X1 = moisture content and X2 = sweetness.
a. Determine the correlation between the two x-variables).
(Stat>Basic Stats>Correlation)
Correlation =
b. Determine the regression equation for predicting Y = rating using X2 = sweetness.
Write the estimated equation -
What is the value of SSR(Sweetness), the regression SS for this regression?
c. Determine the regression equation for predicting Y (rating) using X1 = moisture and X2 =
sweetness. In the regression dialog box, list the predictors in the order Moisture Sweetness.
Write the estimated equation -
What is the value of SSR(Sweetness|Moisture)?
d. Compare the coefficient multiplying Sweetness in the models determined in parts a and b.
Specifically, are they equal?
e. Compare the values of SSR(Sweetness) and SSR(Sweetness|Moisture). Are they equal?
f. Determine the correlation between Y and X1, and also find the correlation between Y and X2.
Correlation between Y and X1 =
Correlation between Y and X2 =
g. Using Calc>Standardize, standardize the three variables by listing all three as Input Columns
and as the columns for Store Results. This converts the data to z-scores. Then run the multiple
regression again. Compare the estimated coefficients to the correlatons found in part f.
Important Note: The equality of the coefficients in the standardized regression to the correlation
coefficients only happens if the x-variables are not correlated!