Q2. Perform and Interpret a Multiple Linear Regression

In the previous analysis above, we examined the relationship between executive function and one predictor variable. Here we are interested in how multiple predictors may be combined to predict executive function even better. Specifically, we would like to build a regression model for executive function with two predictor variables that have the highest and second highest correlations with Executive.

Q2A. Perform a multiple linear regression according to the research question above and answer the following questions. Use "ENTER" (the default in SPSS) as the method of adding the predictor variables to the regression model.Report the omnibus regression results.

F( , ) = , p = , Adjusted R² =

Q2B. Select the correct interpretation of the omnibus regression result from Q2A.

Group of answer choices

(a) We fail to reject the null hypothesis; the regression model does not significantly predict executive function.

(b) We reject the null hypothesis; each predictor in the module significantly predicts the outcome variable.

(c) We fail to reject the null hypothesis; neither predictor in the module significantly predicts the outcome variable.

(d) We reject the null hypothesis; the regression model significantly predicts executive function.

Q2C. Report the coefficient test on each predictor variable, including the beta value and p value. Start with the predictor with the higher beta value.

Predictor 1: = , p =

Predictor 2: = , p =

Q2D. Based on the coefficient tests in Q2C, what can be concluded about the predictors?

Group of answer choices

(a) Only one predictor significantly predicts executive function.

(b) Neither predictor significantly predicts executive function.

(c) Both predictors significantly predict executive function.

Q2E. Comparing the simple regression in Q1 and the multiple regression in Q2, what is a correct observation?

Group of answer choices

(a) The simple regression model predicts a higher proportion of the variance in the outcome variable compared to the multiple regression.

(b) The multiple regression model predicts the outcome variable better than the simple regression model.

(c) The multiple regression model has two significant predictors while the simple regression model has one significant predictor only.

(d) Adding an additional predictor does not make any difference in predicting the outcome variable.

Data:

Sub ID	Education	MMSE	Age	Executive
1	16	28	65.8	84.44
2	12	28	66.9	79.88
3	13	29	76.9	80.11
4	8	29	79.9	100.42
5	12	28	84.1	97.59
6	12	29	72.6	89.75
7	16	30	75.6	108.95
8	13	28	79.6	100.00
9	12	26	78.0	100.05
10	14	26	66.3	97.63
11	13	29	65.1	95.63
12	17	30	67.2	98.52
13	12	29	69.0	103.15
14	16	28	78.9	89.73
15	14	26	69.4	91.22
16	20	28	73.6	93.71
17	15	28	78.4	96.87
18	16	30	69.6	101.35
19	16	29	65.8	97.42
20	18	29	69.5	110.68
21	16	28	67.0	107.64
22	14	30	69.9	103.58
23	16	28	68.8	96.67
24	18	29	71.5	108.34
25	18	30	73.8	90.26
26	14	30	71.1	91.85
27	12	30	74.5	99.20
28	18	28	66.6	112.89
29	15	29	70.7	97.22
30	12	29	76.8	111.00
31	12	29	75.4	91.38
32	19	28	66.7	105.13
33	14	30	65.5	102.57
34	16	30	72.8	102.72
35	19	28	76.5	107.08
36	13	28	72.9	96.14
37	18	30	69.7	95.35
38	16	28	68.2	104.15
39	18	27	65.7	104.76
40	16	30	73.4	106.80
41	20	30	65.8	100.89
42	16	30	66.0	110.68
43	20	29	71.4	111.41
44	18	30	75.8	114.54
45	16	30	68.1	117.27
46	12	29	67.5	123.48
47	16	30	67.8	116.20
48	18	30	73.0	108.14
49	16	30	71.9	117.73
50	14	29	68.3	93.19