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The company’s main activities are the development and marketing of people moving equipments, so they have been invited to submit a proposal for the development and installation of a series of cycle trains for a new airport terminal. These trains will be designed to carry out ...view middle of the document...
We can expect that time will increase by 0.228 per passenger.
We will determine whether how well the estimated equation fits the data which is calculated by finding the total sum of squares, sum of squares due to regression and the sum of squares due to error which is also called the coefficient of determination which provides a measure of the goodness of fitness for the estimated regression equation. Table 2, gives the calculated figures for SST = 299.81, SSR=280.68 and SSE=19.13 and the Coefficient of determination or R2 is calculated to be 93.6%. We can conclude from this figure that 93.6% of the variability in time is explained by the linear relationship between the time it took to transport passengers and the amount of passengers. This indeed is a good fit for the regression equation.
Even though our R2 is large, we must not use the regression equation until further analysis of the appropriateness of the assumed model has been conducted. We will test for the significance of the relationship. But first we must find the standard error of estimate, which is 1.00350, meaning that the standard deviation of the actual point to the line is about 1.00%, (the measure of dispersion). We then calculate the estimate standard of deviation which is sb1 equal to the standard mean of the estimate divided by the sum of x1 minus x bar square. This will give us the figure(0.01363) that's needed to calculate the t-test In this test, the purpose is to see whether or not we can conclude that B1 ≠ 0. If the HO is rejected we will conclude that B1 ≠ 0 and that a statistically significant relationship exists between the two variables. However, if we can’t reject, we will have insufficient evidence to conclude that a significance relationship exits. The test statistic t = 16.69 and must be less than 0.5(2) alpha = 0.1. Since the p-value (0.00) is less than α = 0.1, we reject Ho and conclude that B1 is not equal to zero. This evidence is sufficient to conclude that a significant relationship exists between time and passengers.
The F test will be conducted to test for an overall significant relationship. In table 2, the calculate F test is equal to 278.72 and the Fα = 4.38 (α=0.5). Ho is equal to B1 = 0 and Ha is equal to B1 ≠0. We will reject Ho if the F value is greater than or equal to F alpha. Since the F value is equal to 278.72 and is greater F alpha, we reject Ho and conclude that a significant relationship exists between the time and passengers.
We’ve realized that during the presentation, we have left out an important element that contributed to weight which was the passenger’s “luggage”, each with two pieces weighing fifty pounds each. At this time we now go back and factor that element into the model. While inputting the data for the passenger luggage, we’ve encounter that the luggage variables is highly correlated with the passenger variables which is automatically removed from the model equation and now left with...