Question

Question 1:

An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars of this model and collected the following information on the ages (in years) and prices (in hundreds of dollars) of these cars.

Age	3	8	8	3	5	3	6	4
Price	80	22	32	69	57	64	53	63

Find the least squares regression line equation in the form   y ^ = a + b x . Use "Age" as the independent variable and "Price" as the dependent variable.

Round your answers to four decimal places.

y ^ = Enter you answer to the field 1 in accordance to the question statement + ( Enter you answer to the field 2 in accordance to the question statement ) x

  

Predict the price of a 4 year-old car of this model.

Round your answer to one decimal place.

y pred = Enter your answer in accordance to the question statement Enter your answer in accordance to the question statement

Question 2:

A sample data set produced the following information.

n = 13 , ∑ x = 120 , ∑ y = 290 ,   ∑ x y = 3330 ,   ∑ x 2 = 1370 ,   ∑ y 2 = 25695

Calculate the linear correlation coefficient r .

Round your answer to two decimal places.

Question 3:

The following information is obtained from a sample data set.

n = 12 ,   ∑​x = 66 ,   ∑​y = 588 ,   ∑​x y = 2094 ,   ∑​x 2 = 401

Find the estimated regression line.

  y ^ = Enter you answer to the field 1 in accordance to the question statement + ( Enter you answer to the field 2 in accordance to the question statement ) x

Answer 1

1:

Independent variable (X): Age

Dependent variable (Y): Price

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	3	80	9	6400	240
	8	22	64	484	176
	8	32	64	1024	256
	3	69	9	4761	207
	5	57	25	3249	285
	3	64	9	4096	192
	6	53	36	2809	318
	4	63	16	3969	252
Total	40	440	232	26792	1926

The required predicted value is 63.6.

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2:

Answer: 0.29

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3:

For this question we need  ∑ y 2