Introduction to regression

Chapter 3 Introduction to regression 143
3 Copy and complete this table of calculations for a least squares regression (n = 8).
x-values y-values
1 23
2 21
4 20
8 14
9 16
10 9
11 12
15 5
4 Find the least-squares regression line and the correlation coefficient for the data in
question 3. Express your answers to 2 decimal places.
5 Using the least-squares regression line from question 3, copy and complete the following
table of predicted values.
x 3 5 7 9 11 13 15 17 20
y pred
( x – x)
( x – x)
2
( y – y)
( y – y)
2
6 For the least-squares regression line from question 3, find the residuals.
Analysis
1 Consider this data set which measures the sales figures for a new salesperson.
Day 1 2 3 4 5 6 7 8
Units sold 1 2 4 9 20 44 84 124
The least-squares regression yielded the following equation:
Units sold = 16.7 × day − 39.1
The correlation coefficient was 0.90.
a Do the data exhibit any pattern, and if so what pattern?
b Comment on using the regression line to predict for small values of the independent
variable.
c Use the regression line to predict the sales figures for the 10th day.
2 Transform the data from question 1 using a parabolic (x 2 ) transformation.
3 Perform least-squares regression on the transformed data from question 2.
( x – x)
( y – y)
3C
3C
3E
3E