1. Write down the multiple linear regression model from the regression analysis result. 2. This model is able to explain % of the observed variability in using its linear relationship with the other variables. 3. Interpret the slope coefficient of facebook in context. 4. Interpret the intercept coefficient in context.
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.
In R [datarium package], the marketing dataset contains the impact of the
amount of money spent on three advertising medias (youtube, facebook and
newspaper) on sales. We want to build a model for estimating sales (y) based on the advertising budget invested in youtube (x1), facebook (x2) and newspaper (x3). Use the output provided to answer the questions below. After some trial and error, the following model was fit(Model 1 image).
1. Write down the multiple linear regression model from the
2. This model is able to explain % of the observed variability in using its linear relationship with the other variables.
3. Interpret the slope coefficient of facebook in context.
4. Interpret the intercept coefficient in context.
5. Comment on the overall significance of the model, at a 0.05 significant level.
6. Design and conduct a hypothesis test to check if the variable
newspaper in the context is significant, at a 0.05 significant level. (State your null hypothesis, test statistic, critical value, decision rule, conclusion)
You may use the critical values as below:
t(0.025,196)= 1.972141, t(0.05,196)= 1.652665, t(0.025,3)= 3.182446,
t(0.025,3)= 2.353363.
Now we drop variable newspaper (x3) and introduce the interaction effects between youtube (x1) and facebook (x2), to fit a new multiple linear regression model. The output is shown as in Model 2 image.
7. Write down the new multiple linear regression model from the regression analysis result.
8. Interpret the slope coefficient of the interaction effects between youtube (x1) and facebook (x2) in context.
9. Which model would be a better fit? The old one or the new one? Why?
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