In: Math
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 |
Model |
Dependent variable |
Independent variables |
Model 7 |
read_ability |
age, mem_span, IQ |
When age = 6, mem_span = 4.2 and IQ = 91.
Which model did you select and why?
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:
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 |
Reading_ability=-0.105785293+0.466049243*age+0.26936905*memory_span+0.024640192*IQ
F | Significance F |
26.982191 | 1.69738E-06 |
p<0.05
Regression model is significant.
R sq=0.834960644
=0.835
83.5% variation in reading_ability is explained by model.
Lower 95% | Upper 95% | |
age | 0.207971507 | 0.72412698 |
memory_span | -0.223583037 | 0.762321138 |
IQ | -0.007151972 | 0.056432356 |