Simple Linear Reessionl sovenal used Mitsabishi Mirmge cans Classified ads in a

Question

Simple Linear Reessionl sovenal used Mitsabishi Mirmge cans Classified ads in a newspaper offered several used Mitsubishi Mirage cars for sale. Lis the advertised prices ted below is a random sample of 15 cars showing their ages and Price (S) $13999 S13495 $12999 $9500 S10495 Price (S) $8995 S9495 $6999 6950 Age (vrs) 8 Price (S)$6999 S5995 $4950 $7850 13 S2850 56950 S4950 $4495 A simple linear regression of the model PRICE b, +b,AGE was run. Below are the results (computer output): USED Mitsubishi Mirage PRICES REGRESSION FUNCTION & ANOVA FOR PRICE PRICE- 14285.95-959.0459 AGE R-Squared Adjusted R-Squared Standard error of estimate 816.2135 Number of cases used -0.944333 0.94005 p-value Sig Prob F Value Source Regression 1.46918E+08 Residual 8.66066E+06 Total 1.55578E+08 df MS 1 1.46918E+08 220.52950 0.000000 13 666204.50000 14 USED Mitsubishi Mirage REGRESSION COEFFICIENTS FOR PRICE Two-Sided p-value Variable Coefficient Std Error tValue Sig Prob Constant 14285.95000 448.67270 31.84047 0.000000 AGE 959.04590 64.5811914.85024 0.000000* Use the computer output above to respond to the questions below:

Explanation / Answer

a) The esimtated regression equation is

         Price Y = 14285.950 - 959.04590X (AGE)

b) Interpretation of b0:

     Consider age of the car is 0, using the estiamted regression line, the predicted value of y for x = 0 is

        Price Y = 14285.90 - 959.04590(0) = 14285.90

     Interpretation of b1:

             when x = 14, ycap = 14285.90 - 959.04590(14) = 859.2574

              when x = 15, ycap = 14285.90 - 959.04590(15) = -99.7885

       when x increased by one unit, the y decreased by 859.2574-(-99.7885) = 959.0459 which is the value of b1. That is, on average, age 1 year increase the price of the car decreased $959.0459.

c) when b1 is negative, an increase in x will lead to an decrease in y, and a decrease in x will lead to a increase in y. In otherwords, when b1 is negative, the movement in x and y are in the opposite direction. Such a relatioinship between X and Y is called negative linear relationship.

Here b1 is negative. so Price and Age are negative linear relationship.

d) Here Age increases the price of car decrease. we required the year when the car price drop to zero so

           14285.90 - 959.04590(x) =0 ,      x = 14.896 years

e) when Age = 2 then

               Price Y = 14285.950 - 959.04590(2) = 12367.8082

f)

The p-value of constant (b0) is 0.0000 < less than alpha (0.05), we reject H0,

     Thus b0 not equal to zero

The p-value of constant (b1) is 0.0000 < less than alpha (0.05), we reject H0,

     Thus b1 is also not equal to zero

g) R-square value = 0.9443 which is very high and represents strong relation ship between the variables price and age

Thus, The regression equation is good fit (suitable) for the given data.

               

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