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 pertinentdata are:Period, Fertilizer Sales (tons), Number of Mowers Sold (six-week lag)1 1.6 102 1.3 83 1.8 114 2.0 125 2.2 126 1.6 97 1.5 88 1.3 79 1.7 1010 1.2 611 1.9 11 12 1.4 813 1.7 1014 1.6 9a. Determine the correlation between the two variables. Does it appear that a relationship between these variables will yield reasonable predictions? Explain.b. Obtain a linear regression line for the data.c. Predict expected lawn mower sales for the first week in August, given fertilizer sales six weeks earlier of 2 tons.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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
b. Obtain a linear regression line for the data.
c. Predict expected lawn mower sales for the first week in August, given fertilizer sales six weeks earlier of 2 tons.
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