Question

1. The dataset in the table shows the ratings for a teaching assistant as a function of both the class that the teaching assistant taught and the GPA of the student providing the ratings.

Class 1		Class 2		Class 3
Rating	GPA	Rating	GPA	Rating	GPA
3.17	1	3.17	1	7.25	3.667
3.75	2.333	6.67	2.667	2.58	2
6.08	3.667	4.92	2.333	3.17	1.667
9	3	6.67	3.333	3.75	2.667
4.92	1.667	3.75	1.333	4.92	3
7.25	3.333	4.33	1.667	3.17	1.333
5.5	2.333	5.5	3	4.33	3
4.33	1.333	4.33	1.667	5.5	4

1. Assuming you did not have data for GPA, run the appropriate analysis to determine whether the three classes differ on how they rated the teaching assistant. Comment on your results.
2. Including the GPA data in your analyses, run the appropriate analysis to determine whether the three classes differ on how they rated the teaching assistant. Comment on your results.

3. Using the results of part (b), write out the overall regression equation that will predict the ratings for the teaching assistant.

4. For each class, write the regression equation that will predict the ratings for the teaching assistant.

5. What score would you predict for the teaching assistant by a student who has a GPA of 2.0 and is in Class 3?

6. Compute the adjusted means for the three classes.

Rerun the analysis using effect coding and answer the following questions:

7. Copy and paste the table of regression estimates for your model generated by SPSS.  

8. Using information from part (g), write out the overall regression equation.

1. For Class 3, write the regression equation that will predict the ratings for the teaching assistant.

10. What score would you predict for the teaching assistant by a student who has a GPA of 2.0 and is in Class 3?
11. (Bonus problem) Interpret the meaning of the intercepts in parts (c) and (h).

Answer 1

SOLUTION

Assuming we did not have data for GPA, we can run one way ANOVA(Analysis of variance) to determine whether the three classes differ on how they rated the teaching assistant.

Null hypothesis(H₀): There is no significant difference in the mean rating among the three classes

Alternate hypothesis(H₁): There is significant difference in the mean rating among the three classes.

= 5%

The ANOVA table is given below.

Source of variation	d.f	SS	MSS	F	P-value	F critical value
Between Groups	2	5.440558	2.720279	1.062452	0.363465	3.4668
Within groups	21	53.76794	2.560378
Total	23	59.2085

Conclusion: Accept the null hypothesis that there is no significant difference in the mean rating among the three classes.

Including GPA into consideration we get the regression equation for rating as follows.

X=class,   Y=GPA and Z= rating.

Z=3.285-0.812X+1.371Y

ANOVA table from SPSS

Model	Sum of squares	df	Mean square	F	sig
Regression	39.831	2	19.916	21.583	0.000
Residual	19.377	21	0.923
Total	59.208	23

ceofficients

Model	B	Std Error	Beta	t	sig
Contant	3.285	0.692		4.745	0.000
Class	-0.812	0.243	-0.422	-3.341	0.003
GPA	1.371	0.225	0.771	6.105	0.000

Dependent variable :Rating

From the table we see that none of the coefficients are significant.

Hence there is no significant difeerence in rating.

For class 1 the regression equation for rating (assuming X=GPA and Y = rating)

Y= 1.477X + 2.053

For class 2 the regression equation for rating (assuming X= GPA and Y= rating)

Y =1.437X + 1.863

For class 3 the regression equation for rating (assuming X= GPA and Y= rating)

Y = 1.374 X +0.669

score prediction for the teaching assistant by a student who has a GPA of 2.0 and is in Class 3equation

we use the regression equation

X=class,   Y=GPA and Z= rating.

Z=3.285-0.812X+1.371Y

Rating = 3.591 by substituting X=3 and Y=2