Question

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 36 40 43 51 69 Bone Density 359 356 335 333 312 Table Step 1 of 6 : Find the estimated slope. Round your answer to three decimal places. Step 2 of 6 : Find the estimated y-intercept. Round your answer to three decimal places. Step 3 of 6 : Determine the value of the dependent variable y^ at x=0 Step 4 of 6 : Find the estimated value of y when x=42 Round your answer to three decimal places. Step 5 of 6 : Determine if the statement "All points predicted by the linear model fall on the same line" is true or false. Step 6 of 6 : Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

The statistical software output for this problem is:

Hence,

Step - 1: Slope = -1.378

Step - 2: y - Intercept = 404.876

Step - 3: Value of dependent variable = bo = 404.876

Step - 4: Estimated y = 346.993

Step - 5: True

Step - 6: Coefficient of determination = R-sq = 0.882