Below is some of the regression output from a simple regression of the gas mileage (expressed in miles per gallon) (MPG) an automobile gets and the size of the car's engine (expressed in cubic liters) SUMMARY OUTPUT (engine size and MPG) Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 9 ANOVA df SS MS F Significance F Regression 76.9 76.9 26.96 0.001263155 Residual 20.0 2.9 Total Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 37.7 2.493 15.13 1.324E-06 31.83 43.62 Engine Size -4.73 0.911 0.001 Based on the regression output, what is R 2 (or coefficient of determination)? (please express your answer using 2 decimal places)
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.
QUESTION 1
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SUMMARY OUTPUT
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(engine size and MPG)
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Regression Statistics
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Multiple R
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R Square
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Adjusted R Square
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Standard Error
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Observations
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9
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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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76.9
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76.9
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26.96
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0.001263155
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Residual
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20.0
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2.9
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Total
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Coefficients
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Standard 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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37.7
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2.493
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15.13
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1.324E-06
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31.83
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43.62
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Engine Size
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-4.73
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0.911
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0.001
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Based on the regression output, what is R 2 (or coefficient of determination)? (please express your answer using 2 decimal places)
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