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, y^=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	33	43	59	64	65
Bone Density	352	332	324	322	314

a) Find the estimated slope. Round your answer to three decimal places.

b) Find the estimated y-intercept. Round your answer to three decimal places.

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

d) Find the estimated value of y when x=55.9. Round your answer to three decimal places.

e) 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 y^ is given by?

f) 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 :

a) Slope = -0.971

b) Y-intercept = 380.044

c) True

d) estimated value = 325.791

e)  the change in the dependent variable ˆy is = slope = -0.971

f) the coefficient of determination = 0.901