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,y^=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   Bone Density
38   357
43   351
53   326
59   317
63   313

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:

Find the estimated value of y when x=59. Round your answer to three decimal places.

Step 4 of 6:

Find the error prediction when x=59. Round your answer to three decimal places.

Step 5 of 6:

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^.

Step 6 of 6:

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

Answer 1

Step 1 of 6:

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

-1.884

Step 2 of 6:

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

429.237

Step 3 of 6:

Find the estimated value of y when x=59. Round your answer to three decimal places.

318.108

Step 4 of 6:

Find the error prediction when x=59. Round your answer to three decimal places.

8.923

Step 5 of 6:

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^.

1.884 decrease

Step 6 of 6:

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

0.983

	r²	0.983
	r	-0.992
	Std. Error	2.987
	n	5
	k	1
	Dep. Var.	Bone Density
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,578.0325	1	1,578.0325	176.86	.0009
Residual	26.7675	3	8.9225
Total	1,604.8000	4
Regression output				confidence interval
variables	coefficients	std. error	t (df=3)	p-value	95% lower	95% upper
Intercept	429.237
Age	-1.884	0.1416	-13.299	.0009	-2.3343	-1.4328
Predicted values for: Bone Density
		95% Confidence Interval	95% Prediction Interval
Age	Predicted	lower	upper	lower	upper	Leverage
59	318.108	312.592	323.625	307.117	329.099	0.337

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