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) period fertilizer sales (tons) number of mowers sold (six-week lag) 1 1.6 10 8 1.3 7 2 1.3 8 9 1.7 10 3 1.8 11 10 1.2 6 4 2.0 12 11 1.9 11 5 2.2 12 12 1.4 8 6 1.6 9 13 1.7 10 7 1.5 8 14 1.6 9
a. Determine the correlation between the two variables. Does it appear that a relationship exists between these variables will yield good predictions

Answer 1

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