The given data represent the percentage, y, of the population that is divorced for various ages, x, in the United States in 2010 based on sample data obtained from the United States Statistical Abstract in 2012.
Age, x __________________ Percentage Divorced, y
22 ................................... 0.9
27 ................................... 3.6
32 ................................... 7.4
37 ................................... 10.4
42 ................................... 12.7
50 ................................... 15.7
60 ................................... 16.2
70 ................................... 13.1
80 .................................... 6.5
(a) Draw a scatter diagram of the data. What type of relation appears to exist between x and y?
(b) Find the quadratic regression equation y̅ = b0 + b1x + b2x2.
(c) Draw a residual plot against the fitted values, x, and x2. Also, draw a boxplot of the residuals. Are there any problems with the model?
(d) Interpret the coefficient of determination.
(e) Does the F-test indicate that we should reject H0: b1 = b2 = 0? Is either coefficient not significantly different from zero?
(f) Construct and interpret a 95% confidence interval for percent divorced among all 30 years olds.