Now, the predictors flyer and display were added to the dataset and a multiple linear regression model was fitted. Part of the R output is shown below Estimate Standard Error Intercept 81.23 35.24 Price -0.0318 0.023 Flyer 10.21 3.28 Display 21.67 13.27 Adj R Square = 78.8% Express the least squares regression model. Interpret the coefficient of Flyer and Display in the context of the problem. 3-Calculate a 95% confidence interval of Flyer and interpret the same in the context of the problem. Can we say that promoting a product through fliers significantly affect its sales?
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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- Now, the predictors flyer and display were added to the dataset and a multiple linear regression model was fitted. Part of the R output is shown below
Estimate
Standard Error
Intercept
81.23
35.24
Price
-0.0318
0.023
Flyer
10.21
3.28
Display
21.67
13.27
Adj R Square = 78.8%
- Now, the predictors flyer and display were added to the dataset and a multiple linear regression model was fitted. Part of the R output is shown below
- Express the least squares regression model.
- Interpret the coefficient of Flyer and Display in the context of the problem.
- 3-Calculate a 95% confidence interval of Flyer and interpret the same in the context of the problem. Can we say that promoting a product through fliers significantly affect its sales?
- 4-What is the coefficient of multiple determination of this model? Interpret its value.
- 5-Suppose you want to test whether Price has a positive effect on Sales controlling for Flyer and Display. Carry out an appropriate test at α = .05 and state your conclusion in the context of the problem.
Hypotheses : H0 : Ha :
t=-.0318-0/.023=-1.30
Test statistic :
Degrees of freedom :
Based on the p-value, you would
- Reject H0 at α = 0.01 but not at α = 0.05.
- Reject H0 at α = 0.05 and α = 0.01 but not at α = 0.1.
- Reject H0 at α = 0.05 and α = 0.1 but not at α = 0.01. Reject H0 at α = 0.1 but not at α = 0.01 and α = 0.05.
- Fail to reject H0 at all the above α values.
- Reject H0 at all the above α values.
- Conclusion (in context of the problem)
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