LAB 12 Multiple Linear Regression Complete Solution

Question: #1789

Multiple Linear Regression

1 (9 points—A, B, C, E worth 2 points each)

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 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 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

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. Copy and paste your two scatterplots.

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?

MINITAB: you should have already done this under Multiple Regression by selecting “Graphs” and checking the box for “Residual Plots”.

Solution: #1770

LAB 12 Multiple Linear Regression Complete Solution

The regression equation as can be seen from the above output is, Math Score = 54.1 - 0.484 IQ + 1.02 Abstract_Reas Here as the value 0 for IQ and Abstract reasoning is not on the region based on which the regression model wa...