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 | Number of Mowers Sold |
|--------|------------------|-----------------------|
| 1 | 1.5 | 12 |
| 2 | 1.2 | 10 |
| 3 | 1.7 | 14 |
| 4 | 1.9 | 15 |
| 5 | 2.1 | 16 |
| 6 | 1.4 | 12 |
| 7 | 1.5 | 12 |
| 8 | 1.3 | 10 |
| 9 | 1.8 | 15 |
| 10 | 1.4 | 12 |
| 11 | 1.8 | 15 |
| 12 | 1.3 | 11 |
| 13 | 1.6 | 14 |
| 14 | 1.6 | 13 |

a. Determine the correlation between the two variables. (Round your answer to four decimal points.)

To find the correlation between fertilizer and mower sales, first find the averages for both. Then use these averages and the sales data to calculate the numerator and denominator of the correlation formula. The result is the correlation, which is rounded to four decimal points, indicates the strength and direction of the association between the two variables.

Explanation:

To determine the correlation between the two variables, which are fertilizer sales and mower sales, you will use a statistical method called Pearson's correlation coefficient. The data suggests a probable six-week lag between fertilizer and mower sales, which should be taken into account in the calculation.

First, you would come up with means (averages) for both fertilizer sales and mower sales. Then, for each period, you subtract the mean from respective sales figures, multiply these two results together, and add them all up. This gives you the numerator of your correlation formula. The denominator is a bit more complex: for each period, you square the result of subtracting fertilizer sales mean from actual sales and mower sales mean from actual sales, respectively, sum them all up and take a square root of their product.

After performing the calculation, it is necessary that the final result be rounded to four decimal points. This correlation will give you the strength and direction of the linear relationship between the two variables. A correlation near 1 or -1 shows a strong relationship, while a correlation near 0 shows a weak relationship.

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