Question

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.

A. Build three different regression models the using the variables as shown below. Review the results and determine which is the model is the “best”.

Models	Dependent variable	Independent variables
Model 1	reading_ability	age
Model 2	reading_ability	memory_span
Model 3	reading_ability	iq

1. What is the ANOVA table of the best model?

2. What is the regression equation of the best model?

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

4. What is R² of the best model?

5. For the best model, 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.

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

Answer 1

1. What is the ANOVA table of the best model?

Model 1 is the best model as the R-square is highest for this model as compared to model2 and model3

2. What is the regression equation of the best model?

reading_ability(y)= 3.0323+0.5421*age(x)

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

p-value of the regression model for the model1 is less than typical level of significance alpha=0.05, so Overall Regression Model is significant

4. What is R² of the best model?

R2=0.7157

5. For the best model, what are the 95% confidence intervals for the estimates of the regression coefficients—the B_i’s?

95% confidence interval=(0.3729,0.7113)

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

slope bi is change in dependent variable when unit change is done in independent variable

following regression analysis information has been generated using ms-excel ..

Model 1: using age as independent variable

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.84599
R Square	0.715699
Adjusted R Square	0.699904
Standard Error	0.37661
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	6.426973	6.426973	45.31307	2.61E-06
Residual	18	2.553027	0.141835
Total	19	8.98
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	3.0323	0.492685	6.154649	8.22E-06	1.997209	4.067392
age	0.542132	0.080537	6.731499	2.61E-06	0.372931	0.711333

Model 2: using memory_span as independent variable

Regression Statistics
Multiple R	0.820528
R Square	0.673266
Adjusted R Square	0.655115
Standard Error	0.403737
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	6.045933	6.045933	37.09077	9.37E-06
Residual	18	2.934067	0.163004
Total	19	8.98
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.880316	0.731296	2.57121	0.019227	0.34392	3.416711
memory_span	0.976726	0.160376	6.090219	9.37E-06	0.639788	1.313664

Model 3: using IQ as independent variable

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.150396
R Square	0.022619
Adjusted R Square	-0.03168
Standard Error	0.698287
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.203118	0.203118	0.416562	0.5268
Residual	18	8.776882	0.487605
Total	19	8.98
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	4.719287	2.45411	1.923013	0.070445	-0.43661	9.875181
IQ	0.01638	0.02538	0.645416	0.5268	-0.03694	0.069701