Regression Analysis Trailers versus Boats The regression equ

Regression Analysis: Trailers versus Boats

The regression equation is Trailers = - 166 + 0.577 Boats

Predictor     Coef SE Coef      T      P

Constant   -165.67 52.15    -3.18 0.034

Boats      0.57711 0.08686   6.64 0.003

S = 5.66591   R-Sq = 91.7%   R-Sq(adj) = 89.6%

A) What percentage of variation in the number of trailers purchased is explained by the number of boats purchased?

B) Determine the coefficient of correlation (r) between TRAILERS and BOATS. Is the sign positive or negative?

C) Determine the best-fit linear regression equation for estimating TRAILERS on the basis of BOATS. Identify and interpret the slope of the equation in the context of the question.

D) What would be the estimated number of trailers purchased if 500 boats were purchased?

Solution

A) What percentage of variation in the number of trailers purchased is explained by the number of boats purchased?

R^2=91.7%

--------------------------------------------------------------------------------------------------------

B) Determine the coefficient of correlation (r) between TRAILERS and BOATS. Is the sign positive or negative?

r=sqrt(0.917) =0.9576012

The postive is sign.

--------------------------------------------------------------------------------------------------------

C) Determine the best-fit linear regression equation for estimating TRAILERS on the basis of BOATS. Identify and interpret the slope of the equation in the context of the question.

The regression equation is Trailers = - 166 + 0.577 Boats

The slope is 0.577. When the Boats variable increases one unit, the regression line increases 0.577

--------------------------------------------------------------------------------------------------------

D) What would be the estimated number of trailers purchased if 500 boats were purchased?

- 166 + 0.577*500 =122.5