Respuesta :
Complete question:
Lovely lawns, inc., intends to use sales of lawn fertilizer to predict lawn mower sales. the store manager estimates a probable six-week lag between fertilizer sales and mower sales. the pertinent data are:
Period Fertilizer Sales (tons) Number of Mowers Sold (six-week lag)
1 1.4 9
2 1 7
3 1.5 10
4 1.8 12
5 2.1 13
6 1.5 7
7 1.3 5
8 1.2 5
9 1.6 8
10 1.3 7
11 1.6 11
12 1.3 9
13 1.4 10
14 1.8 12
a. Graph these data to see whether a linear equation might describe the relationship between fertilizer and mowers.
b. Obtain a linear regression line for the data
c. Predict expected lawn mower sales for Period 15, given fertilizer sales six weeks earlier of 2.3 tons.
Solution:
a. Find the attachment for graph
b.
Fertilizer Mowers
x y
1.4 9 1.96 81 12.6
1 7 1 49 7
1.5 10 2.25 100 15
1.8 12 3.24 144 21.6
2.1 13 4.4 116 27.3
1.5 7 2.25 49 10.5
1.35 5 1.69 25 6.5
1.2 5 1.44 25 6
1.6 8 2.56 64 12.8
1.3 7 1.69 49 9.1
1.6 11 2.56 121 17.6
1.3 9 1.69 81 11.7
1.4 10 1.96 100 14
1.8 12 3.24 144 21.6
Σ =20.8 125 31.94 1201 193.3
x = 1.486
y = 8.929
EXY- nXY 193.3- (149.486 -1.486)
Calculated using the formula b =9 = 31 .94 - (14 *1. 486 *1 A86 ) =7.31405
X2 - 7.31405
Calculated using Excel a =Y - bX = 8.929 - 7.31405 *1.486 = -1.938017
Y = a + bx = -1.93802 + 7.31405x
c. Using the formula
Y = a + bx = -1.58678 + 7.033058x
= 14.8843
Using Excel's Forecast
Forecast - 14.58926
The regression equation is -0.672 + 6.158x.
How to calculate the regression equation?
The regression equation is given as:
y = a + bx
where,
x = fertilizer sales
y = mower sales
a = intercept point.
b = slope of regression line
From the complete information, the following can be deduced:
N = 14
Σx = 22.8
Σy = 131
Σx² = 38.18
Σy² = 1269
(Σx)² = 519.84
Σxy = 219.8
(Σy)² = 17161
The slope of the regression line will be:
= [(NΣxy - ΣxΣy)/NΣx² - (Σx)²]
= [(14 × 219.8) - (22.8 × 131)]/[(14 × 38.18) - 519.84]
= 6.158
The intercept will be:
= (Σy - bΣx)/N
= [131 - (6.158 × 22.8)]/14
= -0.672
Therefore, the regression equation is -0.672 + 6.158x.
Learn more about regression on:
https://brainly.com/question/25987747
