Mr. Ali runs a gift shop in the Defense area, Karachi. He advertises weekly in the local newspapers and is considering increasing his advertising budget. Before doing so, he decides to evaluate the past effectiveness of these advertisements. Five weeks are sampled, and the advertising expenses (in PKR) and sales volume for each is shown in the Table 2. Justify if any linearity exists between sales and advertising by finding correlation coefficient values. Develop a regression equation that would help Mr. Ali evaluate his advertising. Perform hypothesis test to check the significance of the results obtained in part b and c. S.No. Sales (PKR 100) Advertising (PKR 100) 1.00 6.00 4.10 2.00 8.00 6.72 3.00 6.00 4.35
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.
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Mr. Ali runs a gift shop in the Defense area, Karachi. He advertises weekly in the local newspapers and is considering increasing his advertising budget. Before doing so, he decides to evaluate the past effectiveness of these advertisements. Five weeks are sampled, and the advertising expenses (in PKR) and sales volume for each is shown in the Table 2.
- Justify if any linearity exists between sales and advertising by finding
correlation coefficient values. - Develop a regression equation that would help Mr. Ali evaluate his advertising.
- Perform hypothesis test to check the significance of the results obtained in part b and c.
|
S.No. |
Sales (PKR 100) |
Advertising (PKR 100) |
|
1.00 |
6.00 |
4.10 |
|
2.00 |
8.00 |
6.72 |
|
3.00 |
6.00 |
4.35 |
Table 2
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