A researcher wants to determine if the nicotine content of a cigarette is related to "tar". A collection of data (in milligrams) on 29 cigarettes produced the accompanying scatterplot, residuals plot, and regression analysis. Complete parts a and b below. ) Explain the meaning of Upper R squared in this context. A. The linear model on tar content accounts for 92.4% of the variability in nicotine content. B. The predicted nicotine content is equal to some constant plus 92.4% of the tar content. C. Around 92.4% of the data points have a residual with magnitude less than the constant coefficient. D. Around 92.4% of the data points fit the linear model.

Answers

Answer 1

Answer:

Answer:

Option A The linear model on tar content accounts for 92.4% of the variability in nicotine content.

Step-by-step explanation:

R-square also known as coefficient of determination measures the variability in dependent variable explained by the linear relationship with independent variable.

The given scenario demonstrates that nicotine content is a dependent variable while tar content is an independent variable. So, the given R-square value 92.4% describes that 92.4% of variability in nicotine content is explained by the linear relationship with tar content. We can also write this as "The linear model on tar content accounts for 92.4% of the variability in nicotine content".

Answer 2

Answer:

Final answer:

The Upper R squared or the coefficient of determination here represents the percentage of the variability in the nicotine content that can be explained by the tar content in the regression model, which in this case is 92.4%.

Explanation:

In this context, the meaning of Upper R squared is represented by option A. The linear model on tar content accounts for 92.4% of the variability in nicotine content. This indicates that 92.4% of the change in nicotine content can be explained by the amount of tar content based on the linear regression model used. This measure is also known as the coefficient of determination. Meanwhile, options B, C, and D are not correct interpretations of the R squared in this context. Both B and D wrongly relate the percentage to the predictability of the data points and option C incorrectly associates this percentage with the residual magnitude.

Learn more about Upper R squared here:

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