Mathematics, 02.03.2020 16:48 groverparham3

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).

Answers: 2

Show answers

Answers

Answer from: aprilpendergrass

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

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

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

Answer from: Quest

step-by-step explanation:

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.