The following data show the advertising expenses(expressed as a percentage of total expenses) and thenet operating profits (expressed as a percentage of totalsales) in a random sample of six drugstores:Advertising Net operatingexpenses profits1.5 3.61.0 2.82.8 5.40.4 1.91.3 2.92.0 4.3 (a) Fit a least squares line that will enable us to predictnet operating profits in terms of advertising expenses.(b) Test the null hypothesis α = 0.8 against the alterna-tive hypothesis α > 0.8 at the 0.01 level of significance.
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.
The following data show the advertising expenses
(expressed as a percentage of total expenses) and the
net operating profits (expressed as a percentage of total
sales) in a random sample of six drugstores:
Advertising Net operating
expenses profits
1.5 3.6
1.0 2.8
2.8 5.4
0.4 1.9
1.3 2.9
2.0 4.3
(a) Fit a least squares line that will enable us to predict
net operating profits in terms of advertising expenses.(b) Test the null hypothesis α = 0.8 against the alterna-
tive hypothesis α > 0.8 at the 0.01 level of significance.
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