Statistics

Statistics

Let us look at an example. You are given the following data set and asked to perform a regression analysis to make a prediction about the data.

x

10

11

12

13

14

y

2

4

6

8

10

∑ −[(∑ )(∑ )] ∑ 2 −(∑ ) 2

The 1st step is to determine the slope,

=

. So we need to find all the values for our

formula.

To do this, we need to know the number of observations or n. In this problem = 5 .

and 2 . We can easily calculate those by creating a table:

Now we need to find the other values:

2

Value

Value

10

2

20 100

11

4

44 121

12

6

72 144

13

8

104 169

14

10

140 196

*For review: is the product of and , for example, 10 × 2 = 20 ; and 2 is the product of x and x, for example, 10 × 10 = 100 .

To calculate slope, we need to find ∑ , ∑ , ∑ , and ∑ 2 (remember, just stands for sum).

∑ = 60 ∑ = 30

•

•

∑ = 380 ∑ 2 = 730

•

•

Now we are ready to solve for the slope. Substitute in the above values into the slope formula.

∑ − [(∑ )(∑ )] ∑ 2 − (∑ ) 2

5(380) − 60(30) 5(730) − (60) 2

100 50

=

=

=

= 2

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