Relationship Between Eighth Grade IQ, Eighth Grade Abstract Reasoning and Ninth grade Math Score
For a statistics class project, students examined the relationship between x1 = 8th grade IQ, x2 = 8th grade Abstract Reasoning and y = 9th grade math scores for 20 students. The data are displayed below.
|
Student
|
Math Score
|
IQ
|
Abstract Reas
|
|
1
|
33
|
95
|
28
|
|
2
|
31
|
100
|
24
|
|
3
|
35
|
100
|
29
|
|
4
|
38
|
102
|
30
|
|
5
|
41
|
103
|
33
|
|
6
|
37
|
105
|
32
|
|
7
|
37
|
106
|
34
|
|
8
|
39
|
106
|
36
|
|
9
|
43
|
106
|
38
|
|
10
|
40
|
109
|
39
|
|
11
|
41
|
110
|
40
|
|
12
|
44
|
110
|
43
|
|
13
|
40
|
111
|
41
|
|
14
|
45
|
112
|
42
|
|
15
|
48
|
112
|
46
|
|
16
|
45
|
114
|
44
|
|
17
|
31
|
114
|
41
|
|
18
|
47
|
115
|
47
|
|
19
|
43
|
117
|
42
|
|
20
|
48
|
118
|
49
|
Open the dataset IQ found in the Datasets folder in ANGEL.
Perform a multiple linear regression with the Response (dependent variable) math score and the variables IQ and Abstract_Reas as the Predictors (independent variables).
Under "Graphs" select "residual plots". The output (excluding plots) should look as follows:
MINITAB: Regression Analysis: Math Score versus IQ, Abstract_Reas
The regression equation is
Math Score = 54.1 - 0.484 IQ + 1.02 Abstract_Reas
Predictor Coef SE Coef T
Constant 54.05 22.99 2.35 0.031
IQ -0.4836 0.2955 -1.64 0.120
Abstract_Reas 1.0185 0.2656 3.84 0.001
S = 3.00271 R-Sq = 70.5% R-Sq(adj) = 67.1%
Analysis of Variance
Source DF SS MS F P
Regression 2 366.92 183.46 20.35 0.000
Residual Error 17 153.28 9.02
Total 19 520.20
a. What is the regression equation and provide an interpretation of each slope in terms of the change in Y per unit change in X
b. Create two scatterplots of the measurements by selecting math score as the response (y-axis), IQ and abstract reasoning as the predictors (x-axis)
Describe the relationship between math score and IQ and math score and abstract reasoning.
c. Based on the output, what are the individual tests of the slopes for this regression equation?
That is, provide the null and alternative hypotheses, the test statistic, p-value of the test, and state your decision and conclusion for each of the two tests for the two slope coefficients.
d. From the output, what is the meaning of the ANOVA F-test?
Provide the two hypotheses (Ho and Ha) statements, decision and conclusion.
e. Check assumptions of constant variance (a scatterplot of the residuals versus the fits(predicted) values) and normality (probability plot).
Copy and paste your residuals vs fits plot and your normal probability plot only.
What are your conclusions based on these graphs?