Question

Find an equation for the least-squares regression line for the following data. Round answers to 3 decimal places (i.e. y = 1.234x -0.123)

Advertising Expenses in 1000's of $ (x): 2.4, 1.6, 2, 2.6, 1.4, 1.6, 2, 2.2

Company Sales in 1000's of $ (y ):225, 184, 220, 240, 180, 184, 186, 215

y=    ?   x+   ?

What would the company sales be if $2500 is spent on advertising?

Answer 1

Solution:
Regression equation can be calculated as
Y = a + bX
a is the intercept of the regression line
b is the slope of the regression line
Y is dependent variable i.e. Company sales
X is an independent variable i.e. Advertising Expenses
The slope of the regression line can be calculated as
Slope b = ((n*Xi*Yi)-(Xi*Yi))/((n*Xi^2)-(Xi)^2)

X	Y	X^2	Y^2	Xy
2.4	225	5.76	50625	540
1.6	184	2.56	33856	294.4
2	220	4	48400	440
2.6	240	6.76	57600	624
1.4	180	1.96	32400	252
1.6	184	2.56	33856	294.4
2	186	4	34596	372
2.2	215	4.84	46225	473
15.8	1634	32.44	337558	3289.8

Slope = ((8*3289.8)-(15.8*1634))/((8*32.44)-(15.8*15.8)) = 501.2/9.88 = 50.729
Intercept of regression line can be calculated as
Intercept = (Yi - Slope*Xi)/n = (1634 - 50.729*15.8)/8 = 104.061
The regression equation is Y = 104.061 + 50.729 * X
Now if $2500 is spent on advertising than company sales be
X = 2.5
So Y = 104.061 + 2.5*50.729 = $230.884
So Company sales 230.884*1000 = $230884, if $2500 is spent on advertising.