Data on the 3-point percentage, field-goal percentage, and...

Data on the 3-point percentage, field-goal percentage, and free-throw percentage for a sample of 50 professional basketball players were obtained. Regression analyses were conducted on the relationships between 3-point percentage and field-goal percentage and between 3-point percentage and freethrow percentage. The StatCrunch results are shown below. (Source: nba.com) Simple linear regression results: Dependent Variable: 3 Point \% Independent Variable: Field Goal \% 3 Point $\%=40.090108-0.091032596$ Field Goal \% Sample size: 50 $\mathrm{R}$ (correlation coefficient) $=-0.048875984$ $\mathrm{R}-\mathrm{sq}=0.0023888618$ Estimate of error standard deviation: $7.7329785$ Simple linear regression results: Dependent Variable: 3 Point \% Independent Variable: Free Throw \% 3 Point $\%=-8.2347225+0.54224127$ Free Throw $\%$ Sample size: 50 $\mathrm{R}$ (correlation coefficient) $=0.57040364$ $\mathrm{R}-\mathrm{sq}=0.32536031$ Estimate of error standard deviation: $6.3591944$ Based on this sample, is there a stronger association between 3 -point percentage and field-goal percentage or 3 -point percentage and freethrow percentage? Provide a reason for your choice based on the StatCrunch results provided.

Data on the 3-point percentage, field-goal percentage, and free-throw percentage for a sample of 50 professional basketball players were obtained. Regression analyses were conducted on the relationships between 3-point percentage and field-goal percentage and between 3-point percentage and freethrow percentage. The StatCrunch results are shown below. (Source: nba.com)
Simple linear regression results:
Dependent Variable: 3 Point \% Independent Variable: Field Goal \% 3 Point $\%=40.090108-0.091032596$ Field Goal \% Sample size: 50 $\mathrm{R}$ (correlation coefficient) $=-0.048875984$
$\mathrm{R}-\mathrm{sq}=0.0023888618$
Estimate of error standard deviation: $7.7329785$
Simple linear regression results:
Dependent Variable: 3 Point \% Independent Variable: Free Throw \% 3 Point $\%=-8.2347225+0.54224127$ Free Throw $\%$ Sample size: 50 $\mathrm{R}$ (correlation coefficient) $=0.57040364$
$\mathrm{R}-\mathrm{sq}=0.32536031$
Estimate of error standard deviation: $6.3591944$
Based on this sample, is there a stronger association between 3 -point percentage and field-goal percentage or 3 -point percentage and freethrow percentage? Provide a reason for your choice based on the StatCrunch results provided.

Key Concepts

Simple Linear Regression

Simple linear regression is a statistical method that models the relationship between two continuous variables by fitting a linear equation to observed data. It helps in understanding how the dependent variable changes as the independent variable varies and is useful for prediction and inference on associations.

Correlation Coefficient

The correlation coefficient is a measure of the linear relationship between two variables, with values ranging from -1 to 1. A coefficient closer to 1 or -1 indicates a stronger linear association, while a value near 0 suggests little to no linear relationship. This metric is crucial for assessing the strength and direction of the association between variables.

Coefficient of Determination (R-squared)

The coefficient of determination, commonly known as R-squared, quantifies the proportion of variability in the dependent variable that is explained by the independent variable in the regression model. Higher R-squared values indicate that a greater portion of the variance is accounted for, suggesting a stronger explanatory power of the model.

Strength of Association Interpretation

Interpreting regression output to assess the strength of associations involves comparing metrics such as the correlation coefficient and R-squared values from different regression models. These measures indicate which independent variable has a more substantial relationship with the dependent variable, guiding conclusions about the relative strength of associations in the data.

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