Q1. Perform and Interpret a Bivariate Linear Regression

This data set contains cognitive function scores and demographics from a group of older adults. The focus of this question set is the executive function (Executive).

Q1A. Perform bivariate (Pearson's) correlations among all the variables in the data set. Report the correlation coefficient and significance value for each of the following pairs of variables:

Education and Executive: r = , p =

MMSE and Executive: r = , p =

Age and Executive: r = , p =

Q1B. Create scatterplot for the strongest correlation from Q1A, with Executive plotted on the Y axis.

Q1C. Perform bivariate (simple) linear regression with Executive as the outcome variable. Use the variable that has the strongest correlation with Executive as the predictor. Report the omnibus regression results.

F( , ) = , p = , Adjusted R² =

Q1D. Select the correct hypothesis testing result.

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

(b) We reject the null hypothesis. The regression model does not significantly predict executive function.

(c) We reject the null hypothesis. The regression model significantly predicts executive function.

(d) We fail to reject the null hypothesis. The regression model significantly predicts executive function.

Q1E. Report the coefficient test on the predictor variable, including the beta value and p value.

= , t = , p =

Q1F. The result from the coefficient test result (Q1E) indicates that ____.

Group of answer choices

(a) The null hypothesis is not rejected; the predictor is significant in predicting executive function.

(b) The null hypothesis is not rejected; the predictor is not significant in predicting executive function.

(c) The null hypothesis is rejected; the predictor is significant in predicting executive function.

(d) The null hypothesis is rejected; the predictor is not significant in predicting executive function.

Q1G. What percentage of the variance in "Executive" can be predicted by this regression model?

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