Question

Question: The table below gives the age and bone density for five randomly selected women. Using this data,...

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 46 48 57 59 68

bone density 353 344 322 320 314

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

Using Excel, go to Data, select Data Analysis, choose Regression. Put Age in X input range and Bone Density in Y input range.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.948
R Square	0.898
Adjusted R Square	0.865
Standard Error	6.220
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1027.152	1027.152	26.553	0.014
Residual	3	116.048	38.683
Total	4	1143.200
	Coefficients	Standard Error	t Stat	P-value
Intercept	430.652	19.615	21.956	0.000
Age (Slope)	-1.799	0.349	-5.153	0.014

1. Slope = -1.799

2. y-intercept = 430.652

3. False

4. value of the dependent variable ˆy at x = 0 = Intercept = 430.652

5. Slope= -1.799

6. coefficient of determination (R-square) = 0.898