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 39 59 60 65 66 Bone Density 338 316 313 312 311 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 if the statement "Not all points predicted by the linear model fall on the same line" is true or false. Step 4 of 6: Find the estimated value of y when x=60. Round your answer to three decimal places. Step 5 of 6: According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable yˆ is given by? 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 :

Step - 1) Slope = -1.023

Step - 2) Y-intercept = 377.152

Step - 3) False

Step - 4) estimated value = 315.749

Step - 5)  the change in the dependent variable ˆy is = slope = -1.023

Step - 6) the coefficient of determination = 0.976