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	3434	3535	4141	4646	5959
Bone Density	349349	340340	325325	320320	318318

Table

Copy Data

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

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	34	349	1156	121801	11866
	35	340	1225	115600	11900
	41	325	1681	105625	13325
	46	320	2116	102400	14720
	59	318	3481	101124	18762
Total	215	1652	9659	546550	70573

Step 3:

All the predicted points fall on the linear regression line. That is given statement is false.

Step 4:

At x=0 y' is equal to 378.489.

Step 5:

if the value of the independent variable is increased by one unit, then the change in the dependent variable ˆy is :

It is decreased by 1.118.

Step 6:

Answer: 0.710

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