Stat 301 – HW 7 answers
Zach will be adding some notes about commonly missed questions. I’ll post them when I get them.
1. Dressed weight of steers.
Note: most numbers have one more digit that probably should be reported.
Rounding a bit more very acceptable.
a. 1 pt. Intercept: 28.07, slope: 0.568
b. 1 pt. 300 lb live wt: 198.4 lb, 400lb live wt: 255.2 lb
c. 1 pt. (170.9lb, 225.9lb)
d. 1 pt. Yes. 150 lbs is very much less than the model predicts you would get.
e. 1 pt. Intercept: -501.1, linear coefficient: 3.171, quadratic coefficient: -0.00316
f. 1 pt. The quadratic model provides evidence of lack of fit for the linear model.
The p-value for the quadratic coefficient is 0.0394, i.e., less than 0.05.
g. 1 pt. 300 lb live wt: 165.3 lb, 400lb live wt: 260.9 lb
h. 1 pt. The predictions for 300lb differ by 23 lb; those for 400lb differ by 5 lb, much less.
i. 1 pt. Predicting for a 300lb live weight requires extrapolation.
300 lb is beyond the range of the X values used to fit the model.
400 lb live weight is well within the range of X values
j. 1 pt. (128lb, 205lb)
k. 2 pts. These data provide no evidence that the customer was shorted.
What the customer got was well within the predictions from the more reasonable model.
2. Clerical work load
a. 2 pts. The number of checks is more important at predicting the work load.
If you use the range of each X variable: the range in predicted values is:
(1081-334)*0.0468 = 34.9 for checks and (86-30)*0.209 = 11.7 for misc. items
If you use the sd of each X variable: 1 sd increase in X increases the predicted value by:
184*0.0468 = 8.61 for checks and 13.8*0.209 = 2.88 for misc. items
b. 2 pts. Over all 7 variables, checks has the highest std. beta of 0.559; bus tickets is lowest at 0.116
Note: lowest is “closest to zero” because a large negative std. beta is still a large effect.
c. 2 pts. No, there does not appear to be an issue with multicollinearity.
The variance inflation factors (VIF) are small for each of the variables.
(checks has the highest VIF at 2.09).
d. 2 pts. Yes, there are concerns about extrapolation when predicting X2 and X3.
The se pred values for X2 and X3 are 4.3 and ca 5 times the smallest se pred (at X mean).
The se pred for X1 is less than twice the smallest se pred, so extrapolation is not a concern.