Linear Estimation of Reading Ability of a Child on Age, Memory Span, and IQ

Name: Project 3 – MGSC 331 Summer
2019
Linear Estimation of Reading ability of a child on age, memory
span, and IQ
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Name: Project 3 – MGSC 331 Summer
2019
1. "What is the ANOVA table of the best model”?
ANS: The best regression model was reading ability estimated by age with R2 = 0.716,
implying that age of children in the sample was able to explain 71.6% variation in reading
ability. The corresponding ANOVA table has been provided underneath.Table 1: ANOVA table of regression model of reading ability on age
df SS MS F
Significance
F
Regressio
n 1 6.427 6.427 45.313 0.000
Residual 18 2.553 0.142
Total 19 8.980
2. “What is the regression equation of the best model”?
ANS: The estimated regression equation is Reading ability = 3.032 +Age * 0.542
3. “Conduct the test for the significance of the Overall Regression Model for the best model”?
ANS:
Null hypothesis: H0: ( β=0 ) : The regression model without any predictor fits the data
equally well (model with constant only fits equally good compared to model with the
predictor age).
Alternate hypothesis: H0: ( β≠0 ) : The regression model with age as predictor fits better
than the constant only model.
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Name: Project 3 – MGSC 331 Summer
2019
Level of significance: 5%
Test statistics: F = 45.313, and p-value < 0.05.
Conclusion: The sample data with age as the predictor provides sufficient substantiation to
infer that the overall regression model fits better compared to the constant only model.
4. “What is R2 of the best model”?
ANS: The best regression model was reading ability estimated by age with R2 = 0.716
5. “For the best model, what are the 95% confidence intervals for the estimates of the regression
coefficients—the Bi’s”?
ANS: The 95% confidence interval for Bi of age was [0.373, 0.711], implying that there was
95% chance that regression coefficient of age would be somewhere between 0.373 and 0.711.
6. “Provide an interpretation of the slopes, bi’s”.
ANS: The regression slope for age was β1 = 0.542, which implied that for increase in age of a
child by one year would increase his/ her reading ability by 0.542 units.
1. “What is the ANOVA table of the best model”?
ANS: The best regression model was reading ability estimated by age and IQ of children.Table 2: ANOVA table of regression model of reading ability on age and IQ
df SS MS F
Significance
F
Regression 2.000 7.374 3.687 39.018 0.000
Residual 17.000 1.606 0.094
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Name: Project 3 – MGSC 331 Summer
2019
Total 19.000 8.980
2. “What is the regression equation of the best model”?
ANS: The estimated regression equation is Reading ability = Age * 0.584 + IQ * 0.036 –
0.703.
3. “Conduct the test for the significance of the Overall Regression Model for the best model”?
ANS:
Null hypothesis: H0: ( β1=β2=0 ) : The regression model without any predictors fits the
data equally well compared to the model with predictors (age and IQ).
Alternate hypothesis: H0: The regression model with age and IQ as predictors fits better than
the constant only model, and at least one βi is non-zero.
Level of significance: 5%
Test statistics: F = 39.018, and p-value < 0.05.
Conclusion: The sample data with age and IQ as predictors provide sufficient substantiation to
infer that the overall regression model fits better compared to the constant only model, and
there is at least one non-zero regression coefficient in the model.
4. “What is R2 of the best model”?
ANS: The best regression model with reading ability estimated by age and IQ has R2 = 0.821.
5. “For the best model, what are the 95% confidence intervals for the estimates of the regression
coefficients—the Bi’s”?
ANS: The 95% confidence interval for β1 for age was [0.443, 0.726], and 95% confidence
interval for β2 for IQ was [0.012, 0.060].
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