The following table represents data on the monthly sales of cellphones and wireless headsets. The company believes that these two products are complementary, which means that the headset sales affect positively the cellphones sales. To confirm this hypothesis, the company will conduct a statistical study based on the data presented in the table below. Month Wireless headset Cellphone sales sales (in Million AED) (in Million AED) 1 1566 1066 2 2524 1942 3 1228 862 4 3084 2372 5 4196 2922 6 1264 1022 7 864 1090 8 3772 2572 9 1528 1316 10 2400 1782 11 4292 2956 12 4798 2892 Questions: Construct a simple regression model to predict the monthly cellphone sales by the wireless headset sales. Formulate the hypothesis testing framework to test the model for its statistical significance. Construct the ANOVA table for the regression model. Perform the significance test for α = 0.05 and what conclusion can be drawn from the obtained results?
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 table represents data on the monthly sales of cellphones and wireless headsets. The company believes that these two products are complementary, which means that the headset sales affect positively the cellphones sales. To confirm this hypothesis, the company will conduct a statistical study based on the data presented in the table below.
|
Month |
Wireless headset |
Cellphone |
|
sales |
sales |
|
|
(in Million AED) |
(in Million AED) |
|
|
1 |
1566 |
1066 |
|
2 |
2524 |
1942 |
|
3 |
1228 |
862 |
|
4 |
3084 |
2372 |
|
5 |
4196 |
2922 |
|
6 |
1264 |
1022 |
|
7 |
864 |
1090 |
|
8 |
3772 |
2572 |
|
9 |
1528 |
1316 |
|
10 |
2400 |
1782 |
|
11 |
4292 |
2956 |
|
12 |
4798 |
2892 |
Questions:
- Construct a simple regression model to predict the monthly cellphone sales by the wireless headset sales.
- Formulate the hypothesis testing framework to test the model for its statistical significance.
- Construct the ANOVA table for the regression model.
- Perform the significance test for α = 0.05 and what conclusion can be drawn from the obtained results?
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