Question

Number of sales people working	Sales​ (in $1000)
33	1111
44	1212
55	1414
99	1515
1111	1818
1111	2020
1313	2020
1414	2222
1616	2222
2020	2626
x overbarxequals=10.610.6	y overbaryequals=1818
​SD(x)equals=5.485.48	​SD(y)equals=4.884.88

Data from a small bookstore are shown in the accompanying table. The manager wants to predict Sales from Number of Sales People Working. Complete parts a through h below.

LOADING...

Click the icon to view the data table.​a) Find the slope​ estimate,

b 1b1.

b 1b1equals=nothing

​(Round to two decimal places as​ needed.)​b) What does

b 1b1

​mean, in this​ context? Select the correct choice below and fill in the answer box to complete your choice.

​(Round to the nearest dollar as​ needed.)

A.On​ average,

​$nothing

is expected when 0 sales people are working.

B.An additional

​$nothing

of sales is associated with each additional sales person working.​c) Find the​ intercept,

b 0b0.

b 0b0equals=nothing

​(Round to two decimal places as​ needed.)​d) What does

b 0b0

mean in this​ context? Is it​ meaningful? Select the correct choice below and fill in the answer box to complete your choice.

​(Round to the nearest dollar as​ needed.)

A.An additional

​$nothing

of sales is associated with each additional sales person working. It is not meaningful because it does not make sense in this context.

B.An additional

​$nothing

of sales is associated with each additional sales person working. It is meaningful in this context.

C.On​ average,

​$nothing

is expected when 0 sales people are working. It is not meaningful because it does not make sense in this context.

D.On​ average,

​$nothing

is expected when 0 sales people are working. It is meaningful in this context.

​e) Write the equation that predicts Sales from Number of Sales People Working.

ModifyingAbove Sales with caretSalesequals=nothingplus+nothingtimes•​(Number

of Sales People​ Working)

​(Round to two decimal places as​ needed.)

​f) If

1818

people are​ working, what Sales do you​ predict?The predicted sales for

1818

people working is

nothing

dollars.

​(Round to the nearest dollar as​ needed.)

​g) If sales are actually

​$25 comma 00025,000​,

what is the value of the​ residual?The value of the residual is

nothing

dollars.

​(Round to the nearest dollar as​ needed.)

​h) Have the sales been overestimated or​ underestimated?

underestimatedunderestimated

overestimatedoverestimated

Click to select your answer(s

Answer 1

a) Find the slope​ estimate.

Slope= 872.78 if we consider sales in actual figures or slope= 0.8728 if we consider the sales in Thousands.

b) What does ​Slope mean, in this​ context? Select the correct choice below and fill in the answer box to complete your choice. ​(Round to the nearest dollar as​ needed.)

B. An additional $872.7811 of sales is associated with each additional sales person working.​

c) Find the​ intercept, ​(Round to two decimal places as​ needed.

Slope= 8748.52 if we consider sales in actual figures or slope= 8.7485 if we consider the sales in Thousands.

​d) What does Intercept mean in this​ context? Is it​ meaningful? Select the correct choice below and fill in the answer box to complete your choice. ​(Round to the nearest dollar as​ needed.)

D. On average, $8748.52 is expected when 0 sales people are working. It is meaningful in this context. (the assumption is even if no sales people are working, the bookstore will still generate sales worth $8748.52

​e) Write the equation that predicts Sales from Number of Sales People Working.

Equation of the line-

Y= mX + c

Where- X= independent variable (no of sales people working)

Y= dependent variable (annual sales)

m= slope pf the line

c= intercept or constant of the equation

the equation based on above calculated slope and variable value becomes-

Y= 872.7811 * X + 8748.521 or

Y= 0.8728 * X + 8.7485 where sales are in thousand

f) If 18 people are​working, what Sales do you​ predict? ​(Round to the nearest dollar as​ needed.)

solving the above sales equation for X=18, we get, annual sales, Y= $24,458.58

​g) If sales are actually 25,0000 what is the value of the​ residual? ​(Round to the nearest dollar as​ needed.)

Residual = actual sales- sales estimated from the above calculated equation.

Residual = 25,000 – 24,458.58 = 541.42

​h) Have the sales been overestimated or​ underestimated?

Since the actual sales were higher than the estimated sales, we underestimated the sales