Question

Use the advertised prices for a used car of a particular model to create a linear model for the relationship between a​ car's Year and its Price. Complete parts a through e.

Year   Price ($)
1994   18,194
1994   17,945
1994   16,887
1994   14,447
1995   19,282
1995   19,017
1995   20,849
1995   18,621
1996   22,665
1996   23,081
1997   24,899
1997   25,492
1997   23,703
1997   24,413
1997   23,934

1) Find the equation of the regression line.

​2) Explain the meaning of the slope of the line. Select the correct choice below and fill in the answer box to complete your choice.

A.The slope indicates that for every one Year increase or one Year newer​ model, the Price decreases by ​$nothing.

B.The slope of nothing indicates the Year when the Price of a used car of this model will be​ $0.

C.The slope of nothing is meaningless and should not be interpreted.

D.The slope indicates that for every one Year increase or one Year newer​ model, the Price increases by ​$nothing.

​3) Explain the meaning of the intercept of the line. Select the correct choice below and fill in the answer box to complete your choice.

A.The intercept of ___indicates the Year when the Price of a used car of this model will be​ $0.

B.The intercept of ____indicates the Price at Year 0.

C.The intercept indicates that cars of this model increase in price by $____per Year.

D.The intercept of ____is meaningless and should not be interpreted.

​4) If you want to sell a used car of this particular model from1997​,what price seems​ appropriate?________

​(Round to the nearest dollar as​ needed.)

Answer 1

1)

Sum of X = 29933
Sum of Y = 313429
Mean X = 1995.5333
Mean Y = 20895.2667
Sum of squares (SS_X) = 21.7333
Sum of products (SP) = 55992.8667

Regression Equation = ŷ = bX + a

b = SP/SS_X = 55992.87/21.73 = 2576.3589

a = M_Y - bM_X = 20895.27 - (2576.36*1995.53) = -5120314.7883

ŷ = 2576.3589X - 5120314.7883

2) As here value of slope is positive so for every increase in x, there is corresponding increase in y.

So answer here is D.The slope indicates that for every one Year increase or one Year newer​ model, the Price increases by ​$2576.3589

3) Intercept is the value of y when x is 0

So here answer is

B.The intercept of - 5120314.7883 indicates the Price at Year 0.

4) Here

ŷ = 2576.3589X - 5120314.7883

So for X=1997,

ŷ = (2576.3589*1997) - 5120314.7883=24673.935=24674