7. Below is the Excel output of a regression. SUMMARY OUTPUT Regression Statistics Multiple R 0.9873 R Square 0.9747 Adjusted R Sc 0.9684 Standard Errc 0.1833 Observations 6 ANOVA df SS MS Significance F Regression 5.1877 5.1817 154.2792 0.0002 Residual 4 0.1343 0.0336 Total 5 5.316 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -0.1602 0.3029 -0.5289 0.6248 13.8759886 0.6807 X Variable 1 1.2731 0.1025 12.4209 0.0002 0.9885 1.5577 (a) What is the regression model? (b) If Y represents cost and X represents usage, what does the model tell? (c) What is SSE and R2? (d) Can we conclude at a = 0.05 that X and Y are significantly correlated? Why (e) Find a 95% confidence interval for the slope ß.
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.
Below is the Excel output of a regression.
(a) What is the regression model?
(b) If represents cost and represents usage, what does the model tell?
(c) What is and ?
(d) Can we conclude at that and are significantly
(e) Find a 95% confidence interval for the slope .
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