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# Essays on ANOVA Results - Determining Factors That Influence Other Responses, the Correlation Coefficient Matrix and Analysis the Values Assignment

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The paper “ ANOVA Results - Determining Factors That Influence Other Responses, the Correlation Coefficient Matrix and Analysis the Values" is an informative version of an assignment on statistics. Five variables are considered in this test, the “ intent” variable which represents the buying intentions, has a value that ranges from 1 to 10, the value 1 represents extremely unlikely and 10 represents extremely likely. The variable, in this case, is therefore considered as the dependent variable. Fixed factors that are the categorical variables that have a different effect on the dependent variable include “ nonstop” representing a number of stops, the variable “ deep time” which represents the time of departure and the variable “ food drink” which represents in fright food and drinks.

The variable “ fare raw” is considered as a covariate variable; this means that “ fare raw” is assumed to have a linear correlation with the variable “ intent” . Assumptions are that; the error terms are independent, they are normally distributed with a mean value of zero and their variance remains constant across observations. Descriptive statistics are summarised in appendix 1 and they indicate that there is a difference in mean values across the categories.

Appendix 2 indicates the Levene’ s test for error term variance equality, the significance value of this test is 0.594, this value is greater than 0.05 the null hypothesis that variances are equal is accepted, therefore the assumptions of this test are not violated. Appendix 3 indicates the ANOVA results, values indicated include the sum of squares and factors partial Eta squared, the table below summarises these results: Partial Eta Squared: The partial Eta value indicates the amount of variation that is accounted for by the variable, it indicates the importance and significance of the variable and from the above: “ fare raw” is of great importance because the value is relatively high (0.7477) while “ food drink” is of less importance in the model given that the value is only (0.05). Omega squared: The partial Eta value may be biased when a sample is used and an alternative is the Omega squared value, This value is determined as follows: W squared ={ sum of squares T – [ (k-1)*(MSerror)]}/{sum of squares total + MSerror} the table below summarises the values: Source Type III Sum of Squares df Mean Square Omega squared num stops 223.725042 1 223.725042 0.011456765 dep time 115.0076353 3 38.33587844 0.005789845 food drink 32.02051904 3 10.67350635 0.001525285 fare raw 1568.4707 1 1568.4707 0.080560836 The results indicate that the variable “ foodbank” variable is less important while “ nonstop” and “ fare raw” are important factors in explaining variations in “ intent” . Managerial implications: Implications of these results indicate that buying decisions will be greatly influenced by fares and the number of stops.

Another factor that will influence this is the departure time. Food and drinks, however, will have little effect on buying decisions as indicated by the partial Eta squared and omega squared statistics. Multiple regression: Appendix 4 summarises the multiple regression model estimated, according to these results the model is as follows: Parameter B Intercept 9.059 [numstops=0] 1.140 [numstops=1] 0(a) [deptime=1] -. 448 [deptime=2] . 637 [deptime=3] . 377 [deptime=4] 0(a) [fooddrnk=1] -. 460 [fooddrnk=2] . 048 [fooddrnk=3] . 060 [fooddrnk=4] 0(a) fareraw -. 014 The model is as follows: Intent = 9.059 + 1.140 numstop0 – 0.448 deptime1 + 0.637 deptime2 + 0.377 deptime3 – 0.460 fooddrnk1 + 0.48 fooddrnk2 + 0.060 fooddrnk3 – 0.014 fareraw Eta squared: Parameter Estimates Dependent Variable: Buying intention Parameter B Partial Eta Squared Noncent.

Parameter Observed Power(a) Intercept 9.059 . 857 63.884 1.000 [numstops=0] 1.140 . 297 16.940 1.000 [numstops=1] 0(b) . . . [deptime=1] -. 448 . 032 4.705 . 997 [deptime=2] . 637 . 0 62 6.691 1.000 [deptime=3] . 377 . 023 3.960 . 977 [deptime=4] 0(b) . . . [fooddrnk=1] -. 460 . 033 4.826 . 998 [fooddrnk=2] . 048 . 000 . 507 . 080 [fooddrnk=3] . 060 . 001 . 627 . 096 [fooddrnk=4] 0(b) . . . fareraw -. 014 . 748 44.853 1.000 Question 2: Exploratory Factor Analysis: This analysis is aimed at determining the factors that influence the other responses, exploratory analysis involves determining the correlation coefficient matrix and analysis the values. Factors whose correlation coefficient is high either negative or positive are more likely to be influenced by one factor, those whose correlation coefficients are low are more likely to be influenced by different factors.

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