High School

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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 | 1.6 | 10 |
| 2 | 1.3 | 8 |
| 3 | 1.8 | 11 |
| 4 | 2.0 | 12 |
| 5 | 2.2 | 12 |
| 6 | 1.6 | 9 |
| 7 | 1.5 | 8 |
| 8 | 1.3 | 7 |
| 9 | 1.7 | 10 |
| 10 | 1.2 | 6 |
| 11 | 1.9 | 11 |
| 12 | 1.4 | 8 |
| 13 | 1.7 | 10 |
| 14 | 1.6 | 9 |

a. Determine the correlation between the two variables. Does it appear that a relationship exists between these variables that will yield good predictions?

Answer :

Answer:

correlation between variables (r) = 0.959 and this signifies a positive relationship between the variables

Explanation:

A) Determine the correlation between the two variables

we have to apply simple Linear regression ( least square method )

attached below is the table

Regression equation ( y ) = a + bx

y = dependent variable ( mower )

x = independent variable ( fertilizer)

a = intercept point ( y axis and regression line )

b = slope ( regression line )

From the attached table

N = 14 , Σ x = 22.8,

Σy = 131, Σy^2 = 1269,

Σx^2 = 38.18, (Σx)^2 = 519.84

Σxy = 219.8, (Σy)^2 = 17161

correlation between variables (r) = 0.959 and this signifies a positive relationship between the variables

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Rewritten by : Barada