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	3535	4545	5151	6565	6767
Bone Density	359359	345345	343343	338338	311311

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

2.Find the value of the coefficient of determination. Round your answer to three decimal places.

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

4.Determine the value of the de[endent variable of ^y at x=0

5.According to the equation of the regression line, if the independent variable is increased by one unit what is the change in the dependent variable y?

6.Not all points predicted by the linear model fall on the same line True or False

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

Answer 1

using minitab>stat>Regression

'we have

Regression Analysis: Bone Density versus Age

The regression equation is
Bone Density = 398.2 - 1.121 Age

S = 10.2975 R-Sq = 74.3% R-Sq(adj) = 65.7%

Analysis of Variance

Source DF SS MS F P
Regression 1 918.69 918.687 8.66 0.060
Error 3 318.11 106.038
Total 4 1236.80

1. the estimated slope is -1.121

.Find the value of the coefficient of determination is 0.743

3. the estimated y-intercept 398.199

4the value of the de[endent variable of ^y at x=0 is 398.20

5.According to the equation of the regression line, if the independent variable is increased by one unit then the dependent variable decreases by 1.121 unit

6.Not all points predicted by the linear model fall on the same line , this is True

7.The regression equation is
Bone Density = 398.2 - 1.121 Age

.the dependent variable y = 398.2 - 1.121*1 = 397.079