STAT 321 – Regression and Forecasting
Midterm Assessment – W21
回归和预测作业代写 No clarifying questions permitted. Please read each question carefully. Show your work. Your grade will be influenced by how clearly you
- No clarifying questions permitted.
- Please read each question carefully. Show your work. Your grade will be influenced by how clearly you express your ideas, and how well you organize your solutions.
- For all question in which the F or t table is required, use the closestavailable degrees of freedom.
The following plot and output are from different regression models fit to data on infant birth weight (BWT, in grams) and characteristics of the mother. The explanatory variables are:
- Age: age of mother (yrs),
- Weight: pre-pregnancy weight of mother (kg),
- Race: race of mother (1 = White, 2 = Black, 3 = Other)
- Smoke: smoking status of mother during pregnancy (1 = Yes; 0 = No)
Model 1: 回归和预测作业代写
Call:lm(formula = BWT ~ Weight)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2369.306 228.439 10.372 <2e-16
Weight 9.771 3.777 2.587 0.0104
Residual standard error: 718.2 on 187 degrees of freedom
Model 2:
Call: lm(formula = BWT ~ Race)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3103.74 72.88 42.586 < 2e-16
Race2 -384.05 157.87 -2.433 *******
Race3 ******* 113.68 -2.637 0.00908
Residual standard error: 714.1 on 186 degrees of freedom
Model 3:
Call: lm(formula = BWT ~ Age + Weight + Smoke)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2362.455 300.710 7.856 3.14e-13
Age 7.094 **** 0.715 0.4757
Weight 8.864 **** 2.338 0.0205
Smoke -267.140 **** -2.525 0.0124
Residual standard error: 708.8 on 185 degrees of freedom
Model 4:
Call:lm(formula = BWT ~ Race + Age + Weight + Smoke)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2841.649 321.366 8.842 7.76e-16
Race2 -511.596 157.029 -3.258 0.001338
Race3 -400.558 119.543 -3.351 0.000979
Age -2.036 9.817 -0.207 0.835902
Weight 8.821 3.831 2.303 0.022425
Smoke -400.238 109.209 -3.665 0.000324
Residual standard error: 681.9 on *** degrees of freedom
1) Consider Model 1. 回归和预测作业代写
a) [2] Interpret the Weight parameter estimate in the context of the study.
b) [3] What conclusion can you draw from the p-value associated with the slope parameter? Be sure to state your conclusion in the context of the study.
c) [4] R output for a 95% prediction interval for infant birthweight for a certain mother is given below:
fit lwr upr ****** 1425.558 4270.601
Give the pre-pregnancy weight of the mother. Show your work.
2) Consider Model 2 回归和预测作业代写
(note that Race has been modelled with indicator (0,1) variables)
a) [4] Give a 95% confidence interval for β1. Use the closest available degrees offreedom in the t table.
b) [3] Interpret the interval in a) in the context of the study (that is, I want you todescribe what the calculated values represent, as explained in lessons).
c) [3] Use the t table to find the p-value associated with H0: β1 = 0 (you will only be able to obtain an interval in which the p-value lies).
d) [3] Suppose Race in Model 2 was remodelled as follows:
x1 = {1 if Black; -1 otherwise} x2 = {1 if Other; -1 otherwise}
Give the value of ^β2 for this new model.
3) Consider Model 3. 回归和预测作业代写
a) [3] For which parameterβj,j = 1,2,3 would the associated confidence interval be widest? Justify your answer.
b) Suppose an investigation of multicollinearity associated with the Age variate yields a VIF = 1.613
i) [3] What proportion of the variation in Age is accounted for by Weight and Race?
ii) [2] What do you conclude from the VIF?
iii) [2] In general, if multicollinearity associated with a certain explanatory variable is found to be a problem, what effect will the removal of that variable have on the remaining parameter estimators?
4) [6]
After accounting for Age, Weight and Smoking status, does Race have an effect on birthweight? Answer this question by performing an additional sum of squares test. Be sure to include the null hypothesis, value and degrees of freedom of the test statistic, p-value, and conclusion.
5) [2]
For the test in 4), give the null hypothesis in the form H0 : Aβ = 0
