2009-08-24_210401_regression6

							Q15.10
Boat sales Boat Tlr Sales
      649              207
      619              194
      596              181
      576              174
      585              168
      574              159

SUMMARY OUTPUT

   Regression Statistics
Multiple R   0.957555946
R Square     0.916913389
             0.896141737
Adjusted R Square
             5.665914685
Standard Error
Observations             6

ANOVA
                   df         SS       MS      F   Significance F
Regression                1 1417.09 1417.09 44.14253 0.002664
Residual                  4 128.4104 32.10259
Total                     5   1545.5

              Coefficients Standard Error t Stat P-value Lower 95%Upper 95%          Upper 95.0%
                                                                           Lower 95.0%
Intercept     -165.6688472 52.15391 -3.17654 0.033647 -310.471 -20.8664 -310.471 -20.8664
Boat sales     0.577108387 0.086862 6.643985 0.002664 0.335941 0.818275 0.335941 0.818275

a. line is y=0.577x-165.67
slope means the sales of boat trailer will increase by 577 when the sales of boat increase by 1000.

b. y=0.577*500-165.67=122.83 thousand.

c.
The reason is that people who bought boat may not buy boat trailer.

Q15.36
proportion of the variation in y is explained by the regression equation is 1-(24/143)=83.22%

Q15.38
             motor vehicles Steel
                       12.83     16.06
                       11.52     14.06
                       12.33        14
                       12.15     15.88
                       12.02     13.86

SUMMARY OUTPUT

  Regression Statistics
Multiple R  0.623718401
R Square     0.389024644
             0.185366192
Adjusted R Square
             0.990905859
Standard Error
Observations           5

ANOVA
                  df           SS      MS        F   Significance F
Regression                1 1.875597 1.875597 1.910182 0.260872
Residual                  3 2.945683 0.981894
Total                     4 4.82128

             Coefficients Standard Error t Stat P-value Lower 95%Upper 95%          Upper 95.0%
                                                                          Lower 95.0%
Intercept    -2.732610633 12.67304 -0.21562 0.843109 -43.0639 37.59866 -43.0639 37.59866
motor vehicles1.438341054 1.040698 1.382093 0.260872 -1.87362 4.750305 -1.87362 4.750305

a)
line is y=1.438x-2.733
r=0.624

b)
r^2=0.389, so there are 38.9% variation of steel shipments is explained by equation

c)
y=1.438*12-2.733=14.523 million
Upper 95.0%
Upper 95.0%