A business is evaluating their advertising budget, and wishes to determine the relationship between advertising dollars spent and changes in revenue. Below is the output from their regression. SUMMARY OUTPUT Regression Statistics Multiple R 0.95 R Square 0.90 Adjusted R Square 0.82 Standard Error 0.82 Observations 8 ANOVA df SS MS F Significance F Regression 3 23.188 7.729 11.505 0.020 Residual 4 2.687 0.672 Total 7 25.875 Coefficients Std Error t Stat P-value Lower 95% Upper 95% Intercept 83.91 2.03 41.36 0.00 78.28 89.54 TV ($k) 1.96 0.48 4.10 0.01 0.63 3.29 Radio ($k) 0.76 0.47 1.64 0.18 -0.53 2.05 Newspaper ($k) 1.76 1.93 0.91 0.41 -3.60 7.11 How much revenue should they expect if they spend 6 on TV, 1.2 on Radio, and 1.5 on Newspaper advertising? Select one: a. 83.91 b. 99.22 c. 88.39 d. 15.31
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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SUMMARY OUTPUT
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Regression Statistics
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Multiple R
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0.95
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R Square
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0.90
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Adjusted R Square
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0.82
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Standard Error
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0.82
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Observations
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8
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ANOVA
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df
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SS
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MS
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F
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Significance F
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Regression
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3
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23.188
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7.729
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11.505
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0.020
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Residual
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4
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2.687
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0.672
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Total
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7
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25.875
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Coefficients
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Std Error
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t Stat
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P-value
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Lower 95%
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Upper 95%
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Intercept
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83.91
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2.03
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41.36
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0.00
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78.28
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89.54
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TV ($k)
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1.96
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0.48
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4.10
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0.01
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0.63
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3.29
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Radio ($k)
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0.76
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0.47
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1.64
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0.18
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-0.53
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2.05
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Newspaper ($k)
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1.76
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1.93
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0.91
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0.41
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-3.60
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7.11
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How much revenue should they expect if they spend 6 on TV, 1.2 on Radio, and 1.5 on Newspaper advertising?
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