Psyc 241 – Homework (Correlation & Regression Topics)
These problems refer to the “Honda Data Revised” dataset. In these data, the model of the car has been coded as 0 =
Civic and 1 = Accord (variable name = model2) and the transmission type has been coded as 0 = 5sp and 1 = automatic
(variable name = trans2). This allows these two nominal variables to be included in more complicated multiple regression
analyses.
1) Generate the complete correlation matrix (pairwise elimination for missing data) for the following variables: price,
age, milage, model2, trans2.
2) Which correlation has the largest absolute magnitude? Explain in words how to interpret this correlation, its
squared value, and its p-value. Note: SPSS labels p-values “Sig”.
3) Which correlation has the smallest absolute magnitude (closest to zero)? Explain in words how to interpret this
correlation, its squared value, and its p-value.
4) Use SPSS to produce a scatterplot to predict price from age that includes the best fit regression line. Use the
scatterplot command with additional editing. Adjust both the X and Y axes for reasonable starting values and
intervals. Provide an informative title.
5) Use SPSS to obtain the equation for the best fit regression line to predict Price from Age. You can use the Curve
Fit command or the Regression command. Write the equation out completely in the “Y’ = bX + a” form and explain
in words how to interpret Y’, b, X, and a in the context of this particular example.
6) Solve the prediction equation for the single best estimated price of a 10 year old car.
7) Within what range of prices could you be about 68% confident the actual price of the 10 year old car would fall?
Within what price range could you be 95% confident of finding the actual selling price? What does the relative size
of these confidence intervals tell you?
8) The following SPSS output is from a multiple regression analysis of the relationship between price of cars and the
age, model, and transmission-type. Use this output to estimate
a. The cost of a 10 year old, automatic, Accord. Include a 68% confidence interval for this estimate.
b. The cost of a 10 year old 5sp, Civic. Include a 68% confidence interval for this estimate.
Hint: Price = Constant + (B1*Age) + (B2*Model2) + (B3*Trans2)
For Model2: Civic = 0 and Accord = 1; for Trans2: 1 = automatic and 0 = 5sp
c. Compare the R2 from this model to that from the model in Question 6 that only included Age as a
predictor of price. How much additional Price variation is explained by adding Model and Transmission to
the prediction equation? How does adding these variables affect the size of the SEE?
Model Summary
Model
1
R
R Square
.946a
.895
Adjusted
R Square
.880
Std. Error of
the Es timate
$1,246.274
a. Predic tors: (Constant), TRANS2, MODEL2, AGE
Coefficients a
Model
1
(Constant)
AGE
MODEL2
TRANS2
Unstandardized
Coefficients
B
Std. Error
9141.807
688.202
-900.815
86.142
2295.678
518.408
1616.789
565.432
a. Dependent Variable: PRICE
Standardi
zed
Coefficie
nts
Beta
-.847
.324
.225
t
13.284
-10.457
4.428
2.859
Sig.
.000
.000
.000
.009
9.) The following SPSS output is from a multiple regression analysis of the relationship between final grade in a college
Calculus class and students’ ACT Math and ACT Social Science scores and a nominal variable indicating if a student had
completed High School Calculus (0 = No, 1 = Yes)
a.
Use this output to write out the general prediction equation to predict a student’s final grade from her ACT
Math, ACT Social Science and HS Calculus experience.
b.
Look at the correlation matrix and the p-values (Sig) for each of the 3 predictors. Which seem to be most
strongly related to the college calculus final grade? Does this make intuitive sense?
c.
Solve your prediction equation for a student whose ACT Math = 25, ACT SS = 29, and who did have a HS
Calculus Class.
d.
Write a paragraph in which you discuss how confident you would be in this prediction. (Hint, look at the size of
the SEE with respect to your estimate of the final grade.)
De scri ptive Statistics
Mean
Grade on College Calc.
Final
ACT Math
ACT Social Sc ienc e
Completed HS Calc ulus
St d. Deviat ion
N
79.519
11.217
154
27.110
22.584
.21
4.114
5.445
.41
154
154
154
Correlations
Pearson Correlation
Sig. (1-tailed)
N
Grade on
College
Calc. Final
ACT Math
ACT Social
Science
Completed
HS Calculus
1.000
.304
.216
.287
.304
.216
.287
1.000
.496
.106
.496
1.000
-.068
.106
-.068
1.000
.
.000
.004
.000
.000
.004
.000
.
.000
.096
.000
.
.201
.096
.201
.
154
154
154
154
154
154
154
154
154
154
154
154
154
154
154
154
Grade on College Calc.
Final
ACT Math
ACT Social Science
Completed HS Calculus
Grade on College Calc.
Final
ACT Math
ACT Social Science
Completed HS Calculus
Grade on College Calc.
Final
ACT Math
ACT Social Science
Completed HS Calculus
Model Summary
Model
1
R
.413a
R Square
.171
Adjusted
R Square
.154
Std. Error of
the Estimate
10.316
a. Predictors: (Constant), Completed HS Calculus, ACT
Social Science, ACT Math
Coeffi cientsa
Model
1
(Const ant)
ACT Math
ACT Social Sc ience
Completed HS Calc ulus
Unstandardized
Coeffic ients
B
St d. Error
56.302
5.622
.573
.237
.269
.178
7.460
2.057
a. Dependent Variable: Grade on College Calc. Final
St andardi
zed
Coeffic ien
ts
Beta
.210
.131
.274
t
10.014
2.423
1.509
3.626
Sig.
.000
.017
.133
.000