Question

the table below shows the number of cars sold last month by seven employees at concord motors and thier numbers of year of sales experience

experience /sales

1

experience	sales
1	8
2	6
2	7
4	14
5	9
6	13
8	10

a regression model is fitted to predict the dependent variable using the independent variable. the model is, y=6.94+0.66x. use the model and predict the y value at x=6

b) what is the error of prediction in question a

Answer 1

Experience(X)	Sales(Y)	Estimated Y	e=Est Y-Y
1	8	7.6	-0.4
2	6	8.26	2.26
2	7	8.26	1.26
4	14	9.58	-4.42
5	9	10.24	1.24
6	13	10.9	-2.1
8	10	12.22	2.22
Standard deviation of error e=			2.307351

The standard deviation is calculated using the formula:

$\sqrt{\frac{1}{n}\sum_{i=1}^{n}{(e_i-\bar{e})^2}}$

The Standard error of prediction is given as :

$\sigma \sqrt{1+\frac{1}{n}}=2.307*\sqrt{1+\frac{1}{7}}=2.4667$

Value of y at x=6

6.94+0.66*7=11.56