ANALYSIS

Multivariate Analysis Assignment



Multivariate Analysis Assignment

What is the regression model and regression equation?

Regression Model

The regression model for the given data is;

Sales = a + ß1 Temperature + ß2 Humidity + e

Regression Equation

The regression equation that can be formulated from the given data is;

Sales = -24.112 + 3.513 Temperature + 7.589 Humidity

Is the regression model valid?

The results indicated that the regression model is valid as the value of R2 reached 0.629, which lies in the acceptable range. The regression coefficient indicates that the independent parameters explain the dependent parameter. Additionally, the results showed that the F value is 31.397, with a probability of less than a < 0.01. These results signify that the obtained regression model is highly significant (Peng & So, 2002; Robinson, Duursma, & Marshall, 2005).

For this Regression model the following assumptions were considered:

The normal distribution for the sample slopes,

The errors of the model were normally distributed,

The independent variables are not correlated, and

The independent variables lack multicollinearity.

Is the sample size adequate?

Yes, the sample size is adequate. The normal distributions along with other different parameters were tested for the present sample. The results of these analysis indicated that the skewness and kurtosis of the three variables were -0.49 and -0.68 for the temperature, 0.047 and -0.08 for humidity and for sales it was -0.356 and -0.406. These results suggest that the sample is adequate and is sufficient enough to build the model for this study (Bai & Ng, 2001).

Furthermore, the measurement of sampling adequacy, done through Kaiser-Meyer-Olkin, resulted in a value of 0.524. This obtained value is more than 0.5 which suggests that the chosen sample size was appropriate (Burnett, 2003).

What interpretation do you make of the results?

The base model shows that the variables of temperature and humidity tend to affect the amount given. The computed results show that both the independent variables produce significant effect (a < 0.05) on the dependent variable of the study which is, the number of sales. The comparative analysis of these effects suggests that the impact of temperature is greater than the effect of humidity. This is because the level of significance of temperature (sig = 0.0001) is greater than the significance of humidity (sig = 0.031). An increase of one unit in humidity will increase the amount given by 7.589, whereas, on the other hand, an increase of one unit in the temperature will lead to an increase of 3.513 in the number of sales. However, the non-significant effect of constant in the function indicates that the effect on the number of sales is produced by the variables of temperature and humidity only (Meyers, Gamst, & Guarino, 2006).

Interaction term for earnings and importance:

Is there an interaction effect in the model?

The analysis of the data concluded that the F value is 2.355 with a value of significance value of 0.212 which more than (a = 0.05). This indicates that there is no interaction effect between the variables of earning and importance (Graham, 2000; Becker, ...