Linear Regression

Linear regression analysis calculates a straight line that best represents the relationship between two variables for which measurements are made in ordered pairs.

Calculating Slope and Intercept

To calculate the slope (m) and the y-intercept (b) of the representative line, press [ STAT ]{ m-b }.

The slope appears in the display.
The y-intercept is stored in the t-register. Press [ x~t ] to display the number.

The representative line is:

y = mx + b

Calculating the Correlation Coefficient

To calculate the correlation coefficient, press [ STAT ]{ r }. The correlation coefficient is a measure of how well the representative line fits the two sets of data values.

When the | r | is close to 1, most of the data is on or very near the line, in which case the line is highly representative of the data. However, the validity of the line diminishes as | r | decreases.

Calculating a Predicated Value

If | r | is close to 1, you can use the equation of the line to make valid predications about additional data.

To predict a y value, enter an x value and press { y' }.
To predict an x value, enter a y value and press [ INV ]{ y' }.

Example

A life insurance company has found that the volume of sales varies according to the number of salespeople employed, as shown below.

Number of salespeople (x)= 7, 12, 4, 5, 11, 9
Sales in thousands $/mo. (y)= 99, 152, 81, 98, 145, 112

Perform a linear regression analysis and predict the number of salespeople needed to produce $115,000 in monthly sales. Then, estimate the amount of sales that should be generated by 10 salespeople.

Procedure	Press	Display
Clear display	[ CLEAR ]
Clear registers and select 2-variable	[ STAT ] { CLR } { CS2 }
Begin data entry	7 [ x~t ] 99 [ ∑+ ]
	12 [ x~t ] 152 [ ∑+ ]
	4 [ x~t ] 81 [ ∑+ ]
	5 [ x~t ] 98 [ ∑+ ]
	11 [ x~t ] 145 [ ∑+ ]
	9 [ x~t ] 112 [ ∑+ ]
Slope (m)	{ --> }{ m-b }
y-intercept (b)	[ x~t ]
Correlation coeff.	{ r }
Projected sales for 10 people	10 { y' }
Number of people needed for $115,000	115 [ INV ]{ y' }