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	33	57	62	64	67
Bone Density	359	357	350	334	322

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: Determine the value of the dependent variable ˆy at x = 0.

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 ˆy 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 :

Simple linear regression results: Dependent Variable: y Independent Variable: x y=391.17886 -0.82648158 x Sample size: 5 R (correlation coefficient) = -0.71069698 R-sq=0.5050902 Estimate of error standard deviation: 12.928555 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 391.17886 27.352296 +03 14.3015 0.0007 Slope -0.82648158 0.47233606 3 -1.7497745 0.1785 +

Step - 1) Slope = -0.826

Step - 2) Y-intercept = 391.179

Step - 3) False

Step - 4) b1

Step - 5)  the change in the dependent variable ˆy is = slope = -0.826

Step - 6) the coefficient of determination = 0.505