Question 1
Suppose that the following model was fit to a set of data.
E(
y) =
β0 +
β1x1 +
β2x2The corresponding plot if residuals against predicted values
is shown. Interpret the plot.
◦ It appears that the variance of
ε is not constant.
◦ It appears that a quadratic model would be a better fit.
◦ The residuals appear to be randomly scattered so that no model modifications are necessary.
◦ It appears that the data contain an outlier.
Question 2
A public health researcher wants to use regression to predict the sun safety knowledge of pre-school children. The researcher randomly sampled 35 preschoolers, assigned them to one of two groups, and then measured the following three variables:
SUNSCORE:
y = Score on sun-safety comprehension test
READING:
x
1 = Reading comprehension score
GROUP:
x
2 = 1 if child received a Be Sun Safe demonstration, 0 if not
A regression model was fit and the following residual plot was observed.
Which of the following assumptions appears violated based on this plot?
◦ The mean of the errors is zero
◦ The errors are normally distributed
◦ The variance of the errors is constant
◦ The errors are independent
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