Models help us describe and summarize relationships between variables. Understanding how process variables relate to each other helps businesses predict and improve performance. For example, a marketing manager might be interested in modeling the relationship between advertisement expenditures and sales revenues. Consider the dataset below and respond to the questions that follow: Advertisement ($'000) Sales ($'000) 1068 4489 1026 5611 767 3290 885 4113 1156 4883 1146 5425 892 4414 938 5506 769 3346 677 3673 1184 6542 1009 5088 Construct a scatter plot with this data. Do you observe a relationship between both variables? Use Excel to fit a linear regression line to the data. What is the fitted regression model? (Hint: You can follow the steps outlined on page 497 of the textbook.) What is the slope? What does the slope tell us?Is the slope significant? What is the intercept? Is it meaningful? What is the value of the regression coefficient,r? What is the value of the coefficient of determination, r^2? What does r^2 tell us? Use the model to predict sales and the business spends $950,000 in advertisement. Does the model underestimate or overestimates ales?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Models help us describe and summarize relationships between variables. Understanding how process variables relate to each other helps businesses predict and improve performance. For example, a marketing manager might be interested in modeling the relationship between advertisement expenditures and sales revenues.
Consider the dataset below and respond to the questions that follow:
Advertisement ($'000) Sales ($'000)
1068 4489
1026 5611
767 3290
885 4113
1156 4883
1146 5425
892 4414
938 5506
769 3346
677 3673
1184 6542
1009 5088
- Construct a
scatter plot with this data. - Do you observe a relationship between both variables?
- Use Excel to fit a linear regression line to the data. What is the fitted regression model? (Hint: You can follow the steps outlined on page 497 of the textbook.)
- What is the slope? What does the slope tell us?Is the slope significant?
- What is the intercept? Is it meaningful?
- What is the value of the regression coefficient,r? What is the value of the coefficient of determination, r^2? What does r^2 tell us?
- Use the model to predict sales and the business spends $950,000 in advertisement. Does the model underestimate or overestimates ales?
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