Question

The table below gives the age and bone density for 12 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.

Age	37	41	54	60	67	35	33	65	68	70	55	66
Bone Density	339	334	328	316	311	340	345	320	313	316	320	317

           

Step 1. Find the estimated slope. Round your answer to three decimal places. What does this value mean?

            Answer: ____________________

Step 2. Find the estimated y-intercept. Round your answer to three decimal places.

            Answer: ____________________

Step 3. 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.

            Answer: ____________________

Step 4. Determine the value of the dependent variable y at x = 0.

            A) b0

B) b1

Step 5. Predict the bone density for a woman aged 69.

            Answer: ____________________

Answer 1

The excel calculation sheet is as below

The excel formula to compute slope and intercept are as below

Slope = SLOPE(Y values, X values)

Intercept = INTERCEPT(Yvalues,Xvalues)

Step 1 : Estimated slope = -0.8082 after rounding to 4 decimal places

Step 2: Estimated Intercept= 368.7629

Estimated regression models

Step 3:

The general form the linear regression equation is

Y = Intercept + (slope * X)

Y = 368.7629 - 0.8082X

Step 4: Value of Y at x=0

Y = 368.7629 - (0.8082 * 0)

Y = 368.7629

Estimated value of y for x=0 is 368.7629

Predict the bone density for a woman aged 69

Here x= 69

y = 368.7629 - (0.8082 * 69)

y =424.5287

Predicted value of bone density for woman aged 69 is 424.5287