The use of Linear Regression to estimate demand Functions

Interpretation of the Number of Raspberries sold,
and price against price of strawberries.

Data analysis on: Comparison of the number of Raspberries sold (QHC) to the price of Raspberries (PHC) and the price of Strawberries (PTC) using analysis of variance (ANOVA)

Using 0.05 level of significance, F-statistics, and an Analysis of variance (ANOVA) test, it was established that the df _num value is k-1, or 3 -1, or 2 and the df _den value is T-k, or 14 - 3, or 11. So, with α = 0.05, the critical value of F in this analysis of variance test was F_0.05 (2, 11) = 19.40. Since computed F (F_C) is greater than Tabulated F (F_T), Ho is rejected. This is because the result of the “Analysis of Variance” (ANOVA) shows that the computed F (53.287) is greater than the tabular values of F-statistics (19.40) at 0.05 degree of freedom (2, 11). This means that there is a significant difference between the numbers of Raspberries sold (Q_HC) to the price of Raspberries (P_HC) and the price of Strawberries.

Data analysis on: Correlation of the number of Raspberries sold (QHC) to the price of Raspberries (PHC) and the price of Strawberries (PHC) using coefficient of determination (R^2)

The resultant R Square 0.9064 is very close to 1 which means that the correlation is near normal curve distribution, so, it is interpreted as very high correlation. Thus, in percentile (%), 90.64 is an indicator of significant relationship between the numbers of Raspberries sold (Q_HC) to the price of Raspberries (P_HC) and the price of Strawberries. Finally, the R square of 0.906442055 is very close to the adjusted R square 0. 8894. This means that the regression model fits the data very well.

P-value

The price of Raspberries and the price of Strawberries are not significant in the full regression equation. This is because the p-value of the two variables is not equal to zero.

95% Confidence interval

The regression slope of Px or the confidence interval is very short with -2.584093567 to 0.331654932 which is more closer to zero while Py has-3.141920767 to 6.861760859 is far from zero so Py has significant implication to the Numbers of Raspberries sold.

t-Stat or test statistics

All of the test statistic values were very close to 1.96 which means that the hypothesis is rejected. The test statistics value of the Y-Intercept is z = -9.886221978 / 65.41785143 = -0.151124223. The value falls near in the left rejection region. The test statistics value of Px = -1.126219318 / 0.662373503 = -1.700278337. The value falls near in the left rejection region. The test statistics value of Py = 1.859920046 / 2.272546361 = 0.818429968. The value falls near in the right rejection region

References:

[1] Aczel,Amir D.,(1996) Complete Business Statistics, 3^rd Ed., Irwin/ McGraw-Hill Companies., USA

[2] Babbie, E and Halley, F. 1998. Adventures in Social Research: Data Analysis Using SPSS for Windows 95. California, USA: Pine Forge Press.

[3] Sander, D. and Smidt, R., (2000) Statistics, A first course, sixth Ed. McGraw-Hill Higher Education

[4] Spiegel, M., Schiller, J. and Srinivasan, R.A, (2000) Theory and Problems of Probability and Statistics, second Ed. McGraw-Hill