Evaluate the estimated demand model. a. What is the R2 ? Is it above 90%? 80%? i

Question

Evaluate the estimated demand model. a. What is the R2 ? Is it above 90%? 80%? i. Explain what the R2 means; i.e. how much of the variation in the quantity demanded does the model explain? b. What is the p-level associated with the model’s F-statistic? Is it less than 5%? 10%? What does the significance indicate about the model? c. Inspect the p-levels for all the independent variables. Are they less than 5%? 10%? Interpret the p-levels and explain which variables are statistically significant. d. Omit any insignificant variables and re-run the model

Fresh to Processed Fruit
Year Fresh Fruit CPI-Fresh Fruit $ CPI-Fresh Fruit ¢ CPI-Processed Fruit $ CPI-Processed Fruit ¢ Wages
1980 88.3 84.8 0.848 82.1 0.82 21.02
1981 83.9 89.4    0.894    91.7    0.92    22.39
1982 85.7 99.3    0.993    96.7    0.97    23.43
1983 90.5 95.1    0.951    98.1    0.98    24.58
1984 88.3 105.6    1.056    105.2    1.05    26.43
1985 86.4 116.3    1.163    109.5    1.10    27.74
1986 93.8 118.7    1.187    106.3    1.06    29.46
1987 96.8 132.0    1.320    110.6    1.11    30.97
1988 97.4 143.0    1.430    121.9    1.22    32.19
1989 96.3 152.4    1.524    125.9    1.26    34.21
1990 92.2 172.5    1.725    136.9    1.37    35.35
1991 89.4 193.7    1.937    126.1    1.26    35.94
1992 98.7 185.2    1.852    131.0    1.31    36.57
1993 98.5 189.2    1.892    132.9    1.33    36.96
1994 99.7 203.2    2.032    134.3    1.34    38.78
1995 97.1 200.3    2.003    137.0    1.37    40.61
1996 97.5 234.4    2.344    83.1    0.83    42.30
1997 101.7 236.3    2.363    148.5    1.49    44.57
1998 101.8 246.5    2.465    101.9    1.02    46.74
1999 101.2 266.3    2.663    105.4    1.05    48.83
2000 101.3 258.3    2.583    106.9    1.07    50.73
2001 97.6 265.1    2.651    109.0    1.09    51.41
2002 99.5 270.2    2.702    111.6    1.12    51.68
2003 101.4 279.1    2.791    113.7    1.14    52.68
2004 102.7 286.8    2.868    114.0    1.14    54.06
2005 100.0 297.4    2.974    118.4    1.18    56.19
2006 101.4 315.2    3.152    121.5    1.22    58.41
2007 97.5 329.5    3.295    125.2    1.25    61.36
2008 100.3 345.4    3.454    135.6    1.36    61.52
2009 98.1 324.4    3.244    142.8    1.43    60.09
2010 102.5 322.3    3.223    141.0    1.41    60.24
2011 105.1 333.1    3.331    146.0    1.46    60.97
2012 108.7 336.6    3.366    150.4    1.50    62.24
2013 111.7 343.2    3.432    154.5    1.55    65.47
2014 113.9 359.7    3.597    154.0    1.54    66.63
2015 112.5 352.0    3.520    157.5    1.58    70.70
2016 116.1 359.8    3.598    158.2    1.58    72.71

SUMMARY OUTPUT Regression Statistics Multiple R 0.899738378 R Square 0.80952915 Adjusted R Square 0.792213618 Standard Error 3.485633365 Observations 37 ANOVA df SS MS F Significance F Regression 3 1704.046016 568.0153388 46.7516191 5.55969E-12 Residual 33 400.9381184 12.14963995 Total 36 2104.984135 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 69.59978346 3.785506683 18.38585671 0% 61.8981122 77.3014547 61.8981122 77.30145471 Fresh Fruit P -0.076120451 0.048752793 -1.561355709 13% -0.175308753 0.02306785 -0.175308753 0.023067851 Processed Fruit 0.071041904 0.038038196 1.867646529 7% -0.006347387 0.14843119 -0.006347387 0.148431195 Wages 0.83431284 0.302947218 2.753987458 1% 0.21796209 1.45066359 0.21796209 1.45066359

Explanation / Answer

A) R2 measure the goodness of fit. This means how well our independent variable explain the dependent variable. No it is not above 90%. Approximately it is equal to 81%. R2 measures how much variation in quantity demanded is explained by variables in model.In our case the independent variable explain 81% in dependent variable.

B) P value associated with f statistic is very small approximately equals to 0.0005 . Yes it is less than 5 or 10%.

C) The p value associated with independent variable are 13% for fresh fruit price, 7% for processed fruit, 1% for wages. Except for fresh fruit p value for other variable is less than 10%. Looking at p values and also at calculted value we can say that fresh fruit prices and processed fruit is statistically significant.

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