Question 5

Metatarsus adductus (MA) is a foot condition wherein the front part of the foot turns in. It is a common condition in adolescents, and usually corrects itself. Hallux abducto valgus (HAV) is a deformation of the big toe that is not usually severe in adolescents, but if severe it usually requires surgery. The severity of each of these foot conditions is measured as the angle of deformity, where higher angles indicate greater deformity.

As part of a study concerned with foot health in adolescents, data were collected from 38 patients who had surgery for HAV. The research question of interest in this study was if severity of MA can help to predict the severity of HAV.

Output from an analysis of these data using Microsoft Excel is shown below. Included is a scatterplot, summary output from a simple linear regression, a plot showing the line of best fit, and a plot of the residuals versus MA angles.

Using this output (above):

(a) State the line of best fit obtained from the regression using the output provided. Briefly comment if the assumptions for a simple linear regression model seem reasonable in this analysis from the information you are presented.

(b) Using the computer output for some of the values you need in the calculations, derive a 90% confidence interval for the population slope. Show all of your working.

(c) Use the line of best fit obtained in part (a) to predict

(i) the HAV for an MA angle of 30 degrees and

(ii) the HAV an MA angle of 5 degrees.

Comment briefly if you have any concerns about the accuracy of these predictions.