1 Relationship Between Eighth Grade IQ, Eighth Grade Abstract Reasoning and Ninth grade Math Score For

Multiple Linear Regression

1 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 = 8^th grade IQ, x₂ = 8^th grade Abstract Reasoning and y = 9^th 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 linear regression with the Response (dependent variable) math score and the variables IQ and Abstract_Reas as the Predictors (independent variables). Store/Save the (unstandardized) Residuals and Fitted(Predicted) values. The output 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 P

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

SPSS: Regression Analysis: Math Score versus IQ, Abstract_Reas

Model Summary^b
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.840^a	.705	.671	3.003
a. Predictors: (Constant), Abstract_Reas, IQ
b. Dependent Variable: MathScore

ANOVA^a
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	366.924	2	183.462	20.348	.000^b
	Residual	153.276	17	9.016
	Total	520.200	19
a. Dependent Variable: MathScore
b. Predictors: (Constant), Abstract_Reas, IQ

Coefficients^a
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
Model		B	Std. Error	Beta	t	Sig.
1	(Constant)	54.053	22.991		2.351	.031
	IQ	-.484	.296	-.573	-1.636	.120
	Abstract_Reas	1.019	.266	1.343	3.835	.001
a. Dependent Variable: MathScore

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 scatter plots 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 is the test 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.

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 (Minitab a probability plot or SPSS a Q-Q plot in SPSS). What are your conclusions based on these graphs?

MINITAB: Scatterplot by Graph > Scatter Plot > Simple. Probability plot by Graph > Probability Plot > Single

SPSS Users: Scatterplot by Graphs > Legacy Dialogues > Scatter/Dot > Simple Scatter Q-Q plot by Analyze > Descriptive Statistics > Explore and enter Unstandardized Residuals in Dependent List click Plots and select box for Normal plots with tests

11 years ago

Report issue

1 Relationship Between Eighth Grade IQ, Eighth Grade Abstract Reasoning and Ninth grade Math Score For

NOT RATED

Purchase the answer to view it

solution.doc