Question

Consider the following data set that contains information about a sample of ten 2015 Subaru Outback offered for sale. Vehicle Condition Color Mileage Price x1000miles) S1000) 1 poor silver 13 30 2 average white 22 3 average blue 29 28 4 average green 46 27 5 average silver 47 26 6 average red 50 24 7 good silver 53 23 8 excellent green 56 22 9 poor red 64 21 10 excellent blue 65 20 The scatter plot that summarizes the data with regard to mileage as the input variable and price as the output variable is provided below a. Is there an association between the two variables? If yes, is it positive or negative? There appears to be Select between the two variables b. Use technology to find the equation of the line of best fit, y = mz+b, and the coefficient of determination and interpret the slope, the vertical intercept, and the coefficient of determination. Round the answers to 3 decimal places.) Select an ang is the i. m Select an answer Select is the Select an answer til. hence there is a select an answer linear relation. c. Use the line of best fit to: i. estimate the price of a car with 26500 miles. Answer: dollars Round the answer to the nearest unit.) Hi estimate the mileage of a car whose price is 28500 dollars. Answer: miles (Round the answer to the nearest unit.)

Answer 1

A)

THERE APPEAR TO BE NEGATIVE ASSOCIATION BETWEEN TWO VARIABLES

.......

B)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	445.00	250.00	2782.50	110.00	-526.00
mean	44.50	25.00	SSxx	SSyy	SSxy

Sample size,   n =   10      
here, x̅ = Σx / n=   44.500          
ȳ = Σy/n =   25.000          
SSxx =    Σ(x-x̅)² =    2782.5000      
SSxy=   Σ(x-x̅)(y-ȳ) =   -526.0      
              
estimated slope , m = SSxy/SSxx =   -526/2782.5=   -0.189

intercept,b = y̅-ß1* x̄ =   25- (-0.189 )*44.5=   33.412   
           
Regression line is, Ŷ=   33.412 + (   -0.189   )*x
              

correlation coefficient ,    r = SSxy/√(SSx.SSy) =   -0.951

hence there is negative relationship

R² =    (SSxy)²/(SSx.SSy) =    0.940   
..............

c)

Predicted Y at X=   26.5   is          
Ŷ=   33.41222   +   -0.18904   *26.5=   28.403
so, price of car = 28403

...................

28.5 = 33.41222      -0.189 *x

x = 28.5-33.412)/ 0.189

=25.989

so, mileage = 25989

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Please let me know in case of any doubt.

Thanks in advance!

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