1. R Squared

2. r = -.944

3. r = -.79

4. Which value for Y is a more accurate prediction for the given X value?
y = x
y = x
if x = 15, y = ?
if x = 6, y = ?
y = (15)
y = (6)
y =
y =
Which value for Y is a more accurate prediction for the given X value?

5. To find how well the Line of Best Fit actually fits the data, we can find a number called R-Squared by using the following formula: 1-
Sum of squared distances between the
actual and predicted Y values
actual Y values and their mean

6. For example, here’s how to find the R Squared
value for the data/graph below: X Y 3 40 10 35 11 30 15 32 22 19 26 23 24 28 18 6
Equation for Line of Best Fit: y = .94x
Correlation = -.94

7. Equation for Line of Best Fit: y = .94x + 43.7
Predicted Y Value
Error
Error Squared
Distance between Y values and their mean
Mean distances squared 3 40 10 35 11 30 15 32 22 19 26 23 24 28 18 6
Mean:
Sum:

8. Equation for Line of Best Fit: y = .94x + 43.7
Predicted Y Value
Error
Error Squared
Distance between Y values and their mean
Mean distances squared 3 40
40.88
.88
.77
14.8
219.04 10 35
34.30
-.70
.49
9.8
96.04 11 30
33.36
3.36
11.29
4.8
23.04 15 32
29.60
-2.40
5.76
6.8
46.24 22 19
23.02
4.02
16.16
-6.2
38.44 26
-2.98
8.88 .8
.64 23 24
22.08
-1.92
3.69
-1.2
1.44 28
17.38
-4.62
21.34
-3.2
10.24 18
-.62
.38
-7.2
51.84 6
10.80
-19.2
368.65
Mean:
25.2
Sum:
91.81
855.60

9. 1- 1- 1- 0.11 =.89 91.81 855.60 To calculate “R Squared”…
Sum of squared distances between the
actual and predicted Y values
actual Y values and their mean 1-
91.81
855.60
=.89

10. The value we got for R Squared was .89
OK. Don’t kill me. Remember this was the data/graph we were finding “R Squared” for?
The value we got for R Squared was .89
Here’s a short-cut. To find R Squared…
…Square r X Y 3 40 10 35 11 30 15 32 22 19 26 23 24 28 18 6
r = -.944
r2 = • -.944
r2 = .89

11. R Squared
To determine how well the regression line fits the data, we find a value called R-Squared (r2)
To find r2, simply square the correlation
The closer r2 is +1, the better the line fits the data
r2 will always be a positive number

12. r = -.944
r2 = .89

13. r = -.79
r2 = .62