Calculating the Equation of the Line

To specify the equation of any straight line we need two values:

• The slope or gradient of the line
• The point at which the line cuts the y axis

Calculating the equation of the line needs the same values to be calculated as for the correlation coefficient.  To do this, we can use a spreadsheet with a regression option – in this case, all you have to worry about is interpreting the coefficients, or a calculator, in which case you will need to calculate the extra columns and work out the column totals in order to find the coefficients.

For a straight line equation: 

Slope:

Intercept:

Example 6.1:

We will calculate the regression coefficient for the following data:

Advertising Expenditure(MWK’00)	Sales (MWK’000)
10	22
12	25
18	26
15	30
8	23
17	27
20	32
15	27
11	25
19	29

Since we will wish to find the effect of advertising expenditure on sales, the advertising expenditure is the independent variable x, and the resulting sales are the dependent variable y.

By plotting the scatter chart and fitting the linear trend line, the ‘best fit’ line will be plotted on the chart. It is also possible to display the r ² value and the regression equation on the chart.

Figure 6.3 Scatter Chart of Advertising and Sales

If you don’t have a regression option, or are using a calculator, you need to calculate the means and SDs for x values and the y values, together with  and  and substitute into the formulae on the previous page.

	Advertising Expenditure (MWK hundreds) x	Sales (MWK thousands) y	xy	x2
	10	22	220	100
	12	25	300	144
	18	26	468	324
	15	30	450	225
	8	23	184	64
	17	27	459	289
	20	32	640	400
	15	27	405	225
	11	25	275	121
	19	29	551	361
Total	-	-	3952	2253
Mean	14.500	26.6	-	-
SD	3.879	2.939	-	-

Slope:

Intercept:

Alternatively . . .

Slope:

Hence;  y = 17.4476 + 0.6312x