One Step Fitness, a local gym, is interested in growing its membership. They have hired an ad agency who recommended that they do direct mail to local residents. After mailing repeatedly for 19 weeks, the company wants to figure out if more mail results in more sales. Below is a scatterplot showing how many direct mail pieces were sent out each week and what the sales of gym memberships were for that week, over the course of the 19 weeks of the campaign. The regression line for this scatterplot is shown. The equation of the line is below, as is r-squared. S a l e s = 33.300517 + 0.0224187 ⋅ D i r e c t M a i lS a l e s = 33.300517 + 0.0224187 ⋅ D i r e c t M a i l R 2 = 0.063413R 2 = 0.063413 What do the coordinates of a dot on the scatterplot represent? What is the correlation coefficient, R? Explain how you calculated R. Use the equation of the regression line to predict the number of gym sales when 489 mail pieces were sent out in a given week. Explain how you calculated your prediction. In reality, 50 gym memberships were sold on the week where 489 mail pieces went out. Explain why your prediction did not match this number.
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.
One Step Fitness, a local gym, is interested in growing its membership. They have hired an ad agency who recommended that they do direct mail to local residents. After mailing repeatedly for 19 weeks, the company wants to figure out if more mail results in more sales.
Below is a scatterplot showing how many direct mail pieces were sent out each week and what the sales of gym memberships were for that week, over the course of the 19 weeks of the campaign.
The regression line for this scatterplot is shown. The equation of the line is below, as is r-squared.
S a l e s = 33.300517 + 0.0224187 ⋅ D i r e c t M a i lS a l e s = 33.300517 + 0.0224187 ⋅ D i r e c t M a i l
R 2 = 0.063413R 2 = 0.063413
- What do the coordinates of a dot on the scatterplot represent?
- What is the
correlation coefficient , R? Explain how you calculated R. - Use the equation of the regression line to predict the number of gym sales when 489 mail pieces were sent out in a given week. Explain how you calculated your prediction.
- In reality, 50 gym memberships were sold on the week where 489 mail pieces went out. Explain why your prediction did not match this number.
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