c. Does Vanguard's advertising expenditure have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate p-value. d. Does advertising by its three largest rivals affect sales of Bright Side detergent in a statistically significant way? Explain using the appropriate p-value. d. What fraction of the total variation in sales of Bright Side remains unexplained? What can the marketing director do to increase the explanatory power of the sales equation? What other explanatory variables might be added to this equation? f. What is the expected level of sales each week when Vanguard spends $40,000 per week and the combined advertising expenditures for the three rivals are $100,000 per week?
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 director of marketing at Vanguard Corporation believes that sales of the company's Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergent (R). The marketing director collects 36 weekly observations on S, A and R to estimate the following multiple regression equation:
S = a + bA + cR .
where, S, A, and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10% level or better.
DEPENDENT VARIABLE: S R-SQUARE F-RATIO P-VALUE ON F
OBSERVATIONS: 36 0.2247 4.781 0.0150
VARIABLE PARAMETER STANDARD T-RATIO P-VALUE
ESTIMATE ERROR
INTERCEPT 175086.0 63821.0 2.74 0.0098
A 0.8550 0.3250 2.63 0.0128
R -0.284 0.164 -1.73 0.0927
_______________
c. Does Vanguard's advertising expenditure have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate p-value.
d. Does advertising by its three largest rivals affect sales of Bright Side detergent in a statistically significant way? Explain using the appropriate p-value.
d. What fraction of the total variation in sales of Bright Side remains unexplained? What can the marketing director do to increase the explanatory power of the sales equation? What other explanatory variables might be added to this equation?
f. What is the expected level of sales each week when Vanguard spends $40,000 per week and the combined advertising expenditures for the three rivals are $100,000 per week?
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