Regression Analysis

In this section, the final regression output results are presented. The regression output is for all five key performance parameters of a motor vehicle. The section is arranged into four sub-sections. The first section interprets and discusses all the statistical data produced by regression analysis. Only significant statistical outputs are discussed in detail.Based on the analysis of the results, in the second section the parametric cost model is presented and all the observations made in the previous sections are used again to analyse the model further. The third section presents the results of the verification process used to validate the outputs ofthe parametric cost model. The fourth section presents a sensitivity analysis to determine how uncertaintyaffects the outputs of the model.

4.2.1 Multivariate Regression Output Results

The table below, Table 4.3 contains all the statistical data produced by regression analysis. The results will be broken down into smaller sections according to the sub-groups on the main results table. The very first at the top of the main table contains regression statistics. The table below that called “ANOVA” presents all the results for the analysis of the variance present in the data used for the regression analysis. The big table below this one presents the actual regression outputs that were used in building the parametric cost model.This section is split further into two smaller sections – one that deals with the coefficients and the other one with statistical data.

4.2.1.1 Regression statistics

Having a look at Table 4.2, regression statistics indicate that the correlation between the five key parameters and the dependent parameter Retail Price is positive and very strong. The correlation is indicated by the value for “Multiple R” in Table 4.2, which is 92.8%, indicating a very strong correlation.The positive correlation on the other hand indicates that the slope of the parametric cost model is positive. With thecoefficient of determination “Adjusted R Square”

being 84.9%, this indicates that majority of the variance in Retail Price can be explained by the fivekey parameters combined.

It can be expected that the error between the actual values and the values estimated by the model to be R 58 499. This error translates to 62% for lowest Retail Price value of R 94 990, 15.4% for a median value of R 380 245, and 8.3% for a maximum value of R704 800 in the data used to build the model. Therefore, it is the assertion of the author that on average one can

expect the accuracy of the model to fluctuate around the actual value by approximately 8.3% - 62%.

Table 4.2: Regression Output Results – 5 Key Parameters

Multiple R 0.928

Coefficients Standard Error t Stat P-value Lower 50.0% Upper 50.0%

Intercept -200 347.63 223 421.56 -0.897 0.374 -352 064.32 -48 630.94 Engine Power

(kW) 895.66 447.08 2.003 0.050 592.06 1 199.25

Engine Torque

(N.m) 600.31 88.18 6.808 8.44E-09 540.43 660.19

Engine Capacity

(CC) 30.60 20.74 1.475 0.146 16.51 44.69

maximum Speed

(km/h) 837.74 649.34 1.290 0.203 396.80 1 278.68

Acceleration

0 - 100 km/h (s) 2 965.54 9 672.96 0.307 0.760 -3 602.98 9 534.06

Overall, the regression statisticsindicate a good ability of the key parameters in explainingthe variance in the Retail Price. However, a closer look at the results is required before accepting the model as final.

4.2.1.2 ANOVA – Analysis of Variance

In Table 4.2 below, “ANOVA” presents the analysis of variance pertaining to the data used.

However, only the two most important variables discussed are F and Significance F. The other variables, df, SS, andMS are used to derive F and Significance F. SS is the Sum of Squares, dfthe degrees of freedom associated with the source of variance.MS is the Mean Square, F and Significance Fare used to determine the significance of the regression. For a broader description of the different variables, it is advisable to refer back to the chapter on literature.

The value of the variable Significance F is used to test if the null hypothesis is true if whether all of the coefficients of the parametric cost model are zero. So since F = 67.11, which is

statistically significantly different from zero and Significance F is a very small value (6.15 x 10

-22), it can be concluded that the null hypothesis does not hold true. Furthermore, this means that at least one of the coefficients of the linear regression model will have a coefficient that is not zero.

4.2.1.3 Key parameter coefficients – parametric cost model

The regression equation coefficients table situated below the ANOVA table contains information on the coefficients of the key parameters, standard errors, t-statistic, P-value and the confidence interval at 50% confidence level. The interpretation with regards to the coefficients is as follows:

• With one unit increase in Engine Power, one can expect the Retail value to increase by R 895.66

• With one unit (1 km/h) increase in the Maximum Speed, one can expect the Retail Price to increase by R837.74.

In Table 4.2 above the coefficient of associated with Acceleration is not statistically significantly different from zero following the criteria developed in sub-section 3.3.3. The t-statistic associated with the coefficient of Acceleration is not statistically significantly different from zero since it is equal to 0.307 and the associated P-value is greater that the alpha value of 0.5. This result is verified by looking at the confidence interval indicating that the value of coefficient lies anywhere between -3 603.98 and 9 534.06; this interval clearly includes zero. Therefore, following the criteria developed in Chapter 3, this means that the influence of Acceleration on Retail Price is minimal since its slope is zero. Acceleration is henceforth left out of the regression equation and the resulting parametric cost model.

Table 4.3 below presents the new results without the input parameter, Acceleration. The regression statistics and ANOVA results did not change much from previously. All the coefficients are statistically significantly different from zero as their confidence intervals do not include zero as a possible coefficient. The P-value of all the coefficients associated with the four key parameters is well below the alpha value of 0.5.

Table 4.3: Regression Output Results – 4 Key Parameters

Multiple R 0.928

R Square 0.861

Adjusted R Square 0.851 Standard Error 58 015.71

Observations 60

ANOVA

df SS MS F Significance F

Regression 4 1.15E+12 2.87E+11 85.27 6.51E-23

Residual 55 1.85E+11 3.37E+09

Total 59 1.33E+12

Coefficients Standard Error t Stat P-value Lower 50.0% Upper 50.0%

Intercept -135 901.67 75 066.05 -1.81 0.076 -186 869.76 -84 933.58 Engine Power

(kW) 837.98 402.22 2.08 0.042 564.88 1 111.07

Engine Torque

(N.m) 596.41 86.53 6.89 5.66E-09 537.65 655.16

Engine Capacity

(CC) 31.76 20.23 1.57 0.122 18.02 45.49

Maximum Speed

(km/h) 691.65 437.47 1.58 0.120 394.62 988.68

Therefore our final parametric cost model will take the following form:

Retail Price = -135 901.67 + (837.98 * Engine Power) + (596.41 * Engine Torque) +(31.76 *

Engine Capacity) + (691.65 * Maximum Speed) (5)

Looking at the value of coefficients in the equation, it can be deduced that Engine Power has the strongest influence on outcome of the cost model since the value of its slope is 837.98 followed by Maximum Speed with a slope of 691.65. Engine Capacity has a very minimal influence on the outcome of the cost model.