Math Problem Statement
The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x , for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
Age 47 49 51 58 63 Bone Density 360 353 336 333 332
Find the value of the coefficient of determination. Round your answer to three decimal places.
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistics
Regression Analysis
Correlation
Coefficient of Determination (R-squared)
Formulas
yˆ = b0 + b1x (Equation of a regression line)
R^2 = 1 - (SS_res / SS_tot) (Coefficient of Determination)
Theorems
Linear Regression Theorem
Pearson Correlation Coefficient
Suitable Grade Level
Grades 10-12
Related Recommendation
Linear Regression for Predicting Bone Density from Age Data
Find the Y-Intercept of a Regression Line: Age and Bone Density Data
Understanding Negative Correlation in Bone Density and Age
Interpreting the Slope and Intercept in Cola Consumption and Bone Density Regression
Normal Distribution: Bone Density Scores and Standard Deviations