7.2 Quo 510 Statistics A-Cat

In order to perform the statistical analysis for the sales of refrigerators and transformers required we will use Analysis of Variance (ANOVA) and regression analysis for future production. By doing the test of independence we determine that the required transformers are dependent of the sale of refrigerators. The regression analysis will dictate how much the sale of refrigerators impact the number of transformers required, the difference in sale of refrigerators will explain the variations. Based on predicted sales of refrigerators we will be able to determine in the future how many transformers we will need to produce.

Data provided, the sales figures increasing over the years, lets us establish a time trend and determine that the data belongs to the time series category. Projected data is dependent on the data from the previous years therefor time analysis is appropriate.

The most appropriate tool for analyzing the data we are provided with is Analysis of Variance, it will test the independence or dependence of transformers requirements based on the sales of refrigerators. The regression analysis will help us establish the relationship between the two.

The data that we were provided and stated before is a time series data because numbers of sales are increasing over time. We know that the data is collected for each quarter over a period of 5 years, from 2006-2010, which determines seasonal fluctuation and one quarter each of the 5 years the sales increase, to compare statistical population like in the data we use ANOVA to represent obvious time periods. As we previously stated the to predict sales for upcoming year we must use last years data, there fore time series analysis is best for analyzing this data.

When analyzing the data we must fine the trend component, in this case we will use the mean to analyze data point by finding the means of all the sets in the data. The linear model representations will give us a raw idea of what’s going on with the data and how it is distributed over time. Next we will calculate ratio to trend to determine the seasonal components. We will also calculate regression factor of refrigerators sales, which is also a time series tool that we use to analyze data. Representing the data in this order gives us a step-by-step calculation and outcome of our date in order for us to be able to interpreted in the correct way and determine if our hypothesis is to be accepted or rejected, and how it will improve our operations.

[pic 1]

Time series plot is a visual representation in form of a line graph, to view data. We plot the time on the x-axis and the observation on the y-axis.  We can see that there is an obviuse pattern of refrigerators sold and the transformers required.

Next is the Regression Analysis

R-squared, Coefficient of Determination, is the fraction of the variation in out dependent variable that is predicted by independent variable, it tells us what percentage of the points fall on the Regression Line, 85% of the values for this model. Multiple R is equal to 0.926, which tells us that the linear relationship between the two variables is pretty strong.  We also know our F, which is P-value and it is equal to 108.211, we use [pic 2]this value for our null hypothesis.