Question

The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression liney^=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   Bone Density
36   351
45   339
48   335
57   325
65   320

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:

Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable y^.

Step 4 of 6:

Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.

Step 5 of 6:

Find the estimated value of y when x=57. Round your answer to three decimal places.

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 = -1.079

Step - 2) Y-intercept = 388.145

Step - 3) the change in the dependent variable ˆy is = slope = -1.079

Step - 4) True

Step - 5)  estimated value = 326.666

Step - 6) the coefficient of determination = 0.980