Question

2. You are a member of a group of researchers who study the reading ability of children. You would like to know if any of the following factors have an effect on the reading ability of a child: age, memory span, and IQ. You conduct a pilot study on a small group of 20 children. From the initial finding, you will make recommendations to your group on further research.

   Complete the regression analyses and answer the questions about the models on this paper. Copy and paste Excel output to show how you determined your answers.

   age	memory_span	IQ	reading_ability
   6.7	4.4	95	7.2
   5.9	4	90	6
   5.5	4.1	105	6
   6.2	4.8	98	6.6
   6.4	5	106	7
   7.3	5.5	100	7.2
   5.7	3.6	88	5.3
   6.15	5	95	6.4
   7.5	5.4	96	6.6
   6.9	5	104	7.3
   4.1	3.9	108	5
   5.5	4.2	90	5.8
   6.9	4.5	91	6.6
   7.2	5	92	6.8
   4	4.2	101	5.6
   7.3	5.5	100	7.2
   5.9	4	90	6
   5.5	4.2	90	5.8
   4	4.2	101	5.6
   5.9	4	90	6

3. Build a regression model using the variables as shown below. Review the results and determine which is the model is the “best”.

Model	Dependent variable	Independent variables
Model 7	read_ability	age, mem_span, IQ

1. What is the ANOVA table of the model?

2. What is the regression equation of the model?

3. Conduct the test for the significance of the Overall Regression Model for the model?

4. What is R² of the best model?

5. What are the 95% confidence intervals for the estimates of the regression coefficients—the B_i’s?

6. Provide an interpretation of the slopes, b_i’s.

3. Select one model you would use to explain reading ability. Then use that model to find the

• 95% confidence interval estimate for the mean reading ability
• 95% prediction interval for reading ability

When age = 6, mem_span = 4.2 and IQ = 91.

Which model did you select and why?

Answer 1

Solution:

In excel install analysis toolpak and then go to

Data >Data analysis>Regression

You wil get

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.913761809
R Square	0.834960644
Adjusted R Square	0.804015764
Standard Error	0.304349041
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	3	7.497946581	2.499316	26.982191	1.69738E-06
Residual	16	1.482053419	0.092628
Total	19	8.98
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-0.105785293	1.337916185	-0.07907	0.937959617	-2.942040904	2.730470318
age	0.466049243	0.121740219	3.828227	0.00148182	0.207971507	0.72412698
memory_span	0.26936905	0.232534957	1.158402	0.263698672	-0.223583037	0.762321138
IQ	0.024640192	0.014996974	1.643011	0.119884665	-0.007151972	0.056432356

From output:

1. What is the ANOVA table of the model?

ANOVA
	df	SS	MS	F	Significance F
Regression	3	7.497946581	2.499316	26.982191	1.69738E-06
Residual	16	1.482053419	0.092628
Total	19	8.98

2. What is the regression equation of the model?

Reading_ability=-0.105785293+0.466049243*age+0.26936905*memory_span+0.024640192*IQ

3. Conduct the test for the significance of the Overall Regression Model for the model?

F	Significance F
26.982191	1.69738E-06

p<0.05

Regression model is significant.

4. What is R² of the best model?

R sq=0.834960644

=0.835

83.5% variation in reading_ability is explained by model.

5. What are the 95% confidence intervals for the estimates of the regression coefficients—the B_i’s?

	Lower 95%	Upper 95%
age	0.207971507	0.72412698
memory_span	-0.223583037	0.762321138
IQ	-0.007151972	0.056432356