1. For the following scores,
X Y
1 6
4 1
1 4
1 3
3 1
Sketch a scatter plot and estimate the value of the
Pearson correlation.
b. Compute the Pearson correlation
2. For the following set of scores,
X Y
6 4
3 1
5 0
6 7
4 2
6 4
a. Compute the Pearson correlation.
b. Add 2 points to each X value and compute the correlation for the modified scores. How does adding a constant to every score affect the value
of the correlation?
c. Multiply each of the original X values by 2 and compute the correlation for the modified scores. How does multiplying each score by a constant
affect the value of the correlation?
3. To simplify the weight variable, the women are classified into five categories that measure actual weight relative to height, from 1 � thinnest
to 5 � heaviest. Income figures are annual income (in thousands), rounded to the nearest $1,000.
a. Calculate the Pearson correlation for these data.
b. Is the correlation statistically significant? Use a two-tailed test with � � .05.
Weight (X) Income (Y)
1 125
2 78
4 49
3 63
5 35
2 84
5 38
3 51
1 93
4 44
4. Assume a two-tailed test with � � .05.
(Note: The table does not list all the possible df values. Use the sample size corresponding to the appropriate
df value that is listed in the table.)
a. A correlation of r � 0.30.
b. A correlation of r � 0.25.
c. A correlation of r � 0.20.
5. A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n � 15 college students. The SAT scores have a mean of M � 580
with SS � 22,400, and the GPAs have a mean of 3.10 with SS � 1.26, and SP � 84.
a. Find the regression equation for predicting GPA from SAT scores.
b. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation, r, then find r2.)
c. Does the regression equation account for a significant portion of the variance in GPA? use a=.05 to evaluate the F-ratio.
6. a. One set of 20 pairs of scores, X and Y values, produces a correlation of r � 0.70. If SSY � 150, find the standard error of estimate for the regression line.
b. A second set of 20 pairs of X and Y values produces of correlation of r � 0.30. If SSY � 150, find the standard error of estimate for the regression line.
7. A researcher obtained the following multiple-regression equation using two predictor variables:
Yˆ � 0.5X1 � 4.5X2 � 9.6. Given that SSY � 210, the
SP value for X1 and Y is 40, and the SP value for X2 and Y is 9, find R2, the percentage of variance accounted for by the equation.
3 answers
with SS � 22,400, and the GPAs have a mean of 3.10 with SS � 1.26, and SP � 84.
a. Find the regression equation for predicting GPA from SAT scores.
b. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation, r, then find r2.)
c. Does the regression equation account for a significant portion of the variance in GPA? use a=.05 to evaluate the F-ratio
2 answers