TABLE 13-2 A candy bar manufacturer is interested in trying to estimate how sale

Question

TABLE 13-2

A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:

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1. what is the percentage of the total variation in candy bar sales explained by the regression model?

D. 88.54%

D. 25.66

3. if the price of the candy bar is set at $2, the predicted sales will be

City Price ($) Sales River City 1.30 100 Hudson 1.60 90 Ellsworth 1.80 90 Prescott 2.00 40 Rock Elm 2.40 38 Stillwater 2.90

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Explanation / Answer

We will find an equation of the regression line in 4 steps.

Step 1: Find XY and X2 as it was done in the table below.

Step 2: Find the sum of every column:

X=12 , Y=390 , XY=700 , X2=25.66

Step 3: Use the following equations to find a and b:

a=YX2XXY/nX2(X)2=39025.6612700/625.66122161.386

b=nXYXY/nX2(X)2=670012390/625.66(12)248.193

Step 4: Substitute a and b in regression equation formula

y = a + bx= 161.386 48.193x

Based on this answers are as below

a. 48.19% a is answer

b Here Xbar=2.

Create the following table.

Step 3: Find the sum of numbers in the last column to get.

(xiX¯¯¯)2=1.66 a is answer

c. for x=2

65 c is answer   

X Y XY XX 1.3 100 130 1.69 1.6 90 144 2.56 1.8 90 162 3.24 2 40 80 4 2.4 38 91.2 5.76 2.9 32 92.8 8.41

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