In a simple linear regression model analyzing the impact of temperature (X) on ice cream sales (Y), if the Sum of Squares Total (SST) is 500 and the Sum of Squares Regression (SSR) is 350, what is the proportion of variation in ice cream sales explained by the regression model? And also find the Coefficient of Determination? Question 12Answera.The regression model explains 30% of the variation in ice cream sales, with a Coefficient of Determination significantly greater than the model explains.b.The regression model explains 70% of the variation in ice cream sales, with a Coefficient of Determination same as the model explains.c.The proportion of variation explained cannot be determined from the information provided, but have a Coefficient of Determination same as the model explains.
Question
In a simple linear regression model analyzing the impact of temperature (X) on ice cream sales (Y), if the Sum of Squares Total (SST) is 500 and the Sum of Squares Regression (SSR) is 350, what is the proportion of variation in ice cream sales explained by the regression model? And also find the Coefficient of Determination? Question 12Answera.The regression model explains 30% of the variation in ice cream sales, with a Coefficient of Determination significantly greater than the model explains.b.The regression model explains 70% of the variation in ice cream sales, with a Coefficient of Determination same as the model explains.c.The proportion of variation explained cannot be determined from the information provided, but have a Coefficient of Determination same as the model explains.
Solution
The proportion of variation in ice cream sales explained by the regression model is calculated by dividing the Sum of Squares Regression (SSR) by the Sum of Squares Total (SST). In this case, that would be 350/500 = 0.7 or 70%.
The Coefficient of Determination, also known as R-squared, is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. In this case, since the proportion of variation explained by the model is 70%, the Coefficient of Determination is also 0.7 or 70%.
So, the correct answer is:
b. The regression model explains 70% of the variation in ice cream sales, with a Coefficient of Determination same as the model explains.
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