Question

A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of salespersons.

Salespersons Years of experience Annual sales ($1000s)
1 1 80
2 3 97
3 4 92
4 4 102
5 6 103
6 8 111
7 10 119
8 10 123
9 11 117
10 13 136

1. Develop an estimated regression equation that can be used to predict annual sales given the years of experience.
2. Compute b1 and b0 (to the nearest whole number).
3. Complete the estimated regression equation below.
= + x
4. Use the estimated regression equation to predict annual sales for a salesperson with 9 years of experience (to the nearest whole number).

Answer 1

Answer:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=632-\frac{70^2}{10}=142$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=8128-\frac{70*1080}{10}=568$

And the slope would be:

$m=\frac{568}{142}=4$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{70}{10}=7$

$\bar y= \frac{\sum y_i}{n}=\frac{1080}{10}=108$

And we can find the intercept using this:

$b=\bar y -m \bar x=108-(4*7)=80$

So the line would be given by:

$y=4 x +80$

And in order to find the predicted value for 9 years we can use the model with x =9 and we got:

$y = 4*9 +80=116$

Step-by-step explanation:

Data given

x: 1,3,4,4,6,8,10,10,11,13

y: 80,97, 92,102,103,111,119,123,117,136

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =70$

$\sum_{i=1}^n y_i =1080$

$\sum_{i=1}^n x^2_i =632$

$\sum_{i=1}^n y^2_i =119082$

$\sum_{i=1}^n x_i y_i =8128$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=632-\frac{70^2}{10}=142$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=8128-\frac{70*1080}{10}=568$

And the slope would be:

$m=\frac{568}{142}=4$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{70}{10}=7$

$\bar y= \frac{\sum y_i}{n}=\frac{1080}{10}=108$

And we can find the intercept using this:

$b=\bar y -m \bar x=108-(4*7)=80$

So the line would be given by:

$y=4 x +80$

And in order to find the predicted value for 9 years we can use the model with x =9 and we got:

$y = 4*9 +80=116$