4.03 Linear Regression

18. Draw a best-fit line for the Tonga Trench data. A best fit line is a smooth line that shows the trend of the data; the line does not have to pass through the data points.

A company computes its accounts receivable turnover to be 20. Based on this information, find the average collection period. If the company has a credit collection period of 30 days, explain the relationship between the credit collection period and the average collection period. Average collection period is 18.25. The relationship between the credit collection period and the average collection period is very good for this company. This company will receive payments owed to them prior to them having to pay whom they owe. (http://www.cliffsnotes.com/study_guide/Ratio-Analysis.topicArticleId-21248,articleId-21213.html) (http://www.investopedia.com/terms/a/average_collection_period.asp#axzz2LMPGyktQ)

Slide 17: This curve demonstrates a one-tail hypothesis with the critical region representing 5% showing a negative relationship.

5) Graph the equation you wrote in step four superimposed over the original data. Comment on how well or how poorly the equation fits the data.

The relationship between the variables Years and Credit Balance is illustrated in the following scatter plot:

AJ DAVIS is a department store chain, which has many credit customers. A sample of 50 credit customers is selected with data collected on location, income, credit balance, number of people and years lived in the house

29. A distribution center for a chain of electronics supply stores fills and ships orders to retail outlets. A random sample of orders is selected as they are received and the dollar amount of the order (in thousands of dollars) is recorded, and then the time (in hours) required to fill the order and have it ready for shipping is determined. A scatterplot showing the times as the response variable and the dollar amounts (in thousands of dollars) as the predictor shows a linear trend. The least squares regression line is determined to be: yˆ= 0.76 +1.8x. A plot of the residuals versus the dollar amounts showed no pattern, and the following values were reported: Correlation r +0.90; R 2 = 0.81; standard deviation of the residuals is 0.48. What percentage of the variation in the times required to prepare an order for shipping is accounted for by the fitted line?

There are 50 credit customers who were selected for the data collection on five variables such as location, income, size, years, and credit balance. In order to understand more about their customer, AJ DAVIS must use graphical, numerical summary to be able to interpret and better expand their business in the future.

This dataset contains customer’s default payments in Taiwan. This dataset has 30000 observations and 24 features. The features are all real numbers. There is a binary variable, default payment (Yes=1, No=0), as the response variable. The rest of the 23 features are explanatory variables, including amount of the given credit (X1), history of past payment (X6-X11), amount of bill statement (X12-X17), amount of previous payment (X18-X23), and some demographical data. In predictions, we did not include some of the demographical variables

Using MINITAB perform the regression and correlation analysis for the data on SALES (Y) and CALLS (X), by answering the following questions:

The Political Spectrum consists of four quadrants: Authoritarian Right, Authoritarian Left, Libertarian Left, and Libertarian Right. The "x" axis of this graph represents economics with a left-right scale. The "y" axis depicts the social scale ranging from libertarian to authoritarian. I have been plotted at -3.88 (economic left/right), -3.54 (social libertarian/authoritarian) in the libertarian left quadrant.

The line of best-fit is used to find the gradient, the T2/L value, if straight or linear it shows that the relationship between the two is directly proportional. Using the original equation, you can square both sides and rearrange it to make . Then you can input the gradient value (T2/L) and work out g. , where g equals 10.13 m/s2. This value is close to the

The trendline, known as the line of best fit or the least squares regression line, shows the linear equation which best explains the sums up the data’s trend. The formula on the right is the formula of the line of best fit.

Using TI InterActive!™ to graph that function, overlaid with the original data, and restricting the graph of the function to the same domain and range as the domain and range on the scatterplot, the graph is as follows:

– Predict the value of a dependent variable based on the value of at least one independent variable – Explain the impact of changes in an independent variable on the dependent variable