1. Chapter 5
LSRL

2. Bivariate Data x: explanatory (independent) variable
y: response (dependent) variable
Use x to predict y

3. Be sure to put the hat on the y!
– (y-hat) means predicted y-value
b – slope
the amount y increases when x increases by 1 unit
a – y-intercept
height of the line when x = 0
in some situations, y-intercept has no meaning
Be sure to put the hat on the y!

4. Least Squares Regression Line (LSRL)
Line that gives the best fit to the data
Minimizes the sum of the squared deviations from the line

5. (0,0) (3,10) (6,2) 4.5 -5 -4 (0,0) y =.5(6) + 4 = 7 2 – 7 = -5 y = 4
0 – 4 = -4 -5
y =.5(3) + 4 = 5.5
10 – 5.5 = 4.5 -4
(0,0)
Sum of the squares = 61.25

6. What is the sum of the deviations from the line?
Use a calculator to find the line of best fit
(0,0)
(3,10)
(6,2)
Will it always be zero? 6 -3
The line that minimizes the sum of the squared deviations from the line is the LSRL -3
Sum of the squares = 54

7. Interpretations Slope:
For each unit increase in x, there is an approximate increase/decrease of b in y.
Correlation coefficient:
There is a strength, direction, linear relationship between x and y.

8. The ages (in months) and heights (in inches) of seven children are given.
Find the LSRL.
Interpret the slope and correlation coefficient in the context of the problem.

9. Slope:
For each increase of one month in age, there is an approximate increase of .34 inches in heights of children.
Correlation coefficient:
There is a strong, positive, linear relationship between the age and height of children.

10. Predict the height of a child who is 4.5 years old.
The ages (in months) and heights (in inches) of seven children are given. x y
Predict the height of a child who is 4.5 years old.
Predict the height of someone who is 20 years old.
Graph, find lsrl, also examine mean of x & y

11. Extrapolation
LSRL should not be used to predict y for x-values outside the data set
We don’t know if the pattern in the scatterplot continues

12. This point is always on the LSRL
Age Ht
Calculate x & y.
Find the point (x, y) on the scatterplot.
This point is always on the LSRL
Graph, find lsrl, also examine mean of x & y

13.  Both r and the LSRL are non-resistant measures

14. Formulas on green sheet

15. The following statistics are found for the variables posted speed limit and the average number of accidents.
Find the LSRL & predict the number of accidents for a posted speed limit of 50 mph.