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+b1xy^=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 29 43 46 61 64

BD 352 346 321 314 312

STEP 1: Find the estimated slope.

STEP 2: Find the estimated y-intercept.

STEP 3: Determine the value of the dependent variable y^ at x=0.

STEP 4: Find the estimated value of y when x=64.

STEP 5: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 value.

STEP 6: Find the value of the coefficient of determination.

Answer 1

The statistical software output for this problem is:

Hence,

Step - 1: Slope = -1.197

Step - 2: y - Intercept = 387.150

Step - 3: Value of dependent variable = b0 = 387.150

Step - 4: Estimated value = 310.574

Step - 5: Change in dependent variable = b1 = -1.197

Step - 6: Coefficient of determination = 0.834