A part of the output of a regression analysis of Y against X using Excel is given below: SUMMARY OUTPUT Regression Statistics Multiple R 0.954704 R Square 0.91146 Adjusted R Square 0.896703 Standard Error 28.98954 Observations 8 ANOVA df SS MS F Significance F Regression 1 51907.64 51907.64 Residual 6 5042.361 840.3936 Total 7 56950 Coefficients Standard Error t Stat P-value Intercept 45.2159 39.8049 Age 5.3265 0.6777 a. State the estimated regression line and interpret the slope coefficient
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.
A part of the output of a
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.954704
R Square 0.91146
Adjusted R Square 0.896703
Standard Error 28.98954
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 51907.64 51907.64
Residual 6 5042.361 840.3936
Total 7 56950
Coefficients Standard Error t Stat P-value
Intercept 45.2159 39.8049
Age 5.3265 0.6777
a. State the estimated regression line and interpret the slope coefficient.
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