Correlation And Linear Regression PDF

POLYTECHNIC UNIVERSITY OF THE PHILIPPINES – CABIAO CAMPUS SAN ROQUE, CABIAO, NUEVA ECIJA Chapter IV: CORRELATION AND LINEAR REGRESSION Prepared by: Rogene C. Esguerra...

POLYTECHNIC UNIVERSITY OF THE PHILIPPINES – CABIAO CAMPUS SAN ROQUE, CABIAO, NUEVA ECIJA Chapter IV: CORRELATION AND LINEAR REGRESSION Prepared by: Rogene C. Esguerra The Country’s 1st Polytechnic U Correlation and Linear Regression Learning Target: At the end of the discussion, the students must be able to comprehend and demonstrate the mastery of the following: ❑Understand the concept of correlation. ❑Enumerate some examples of correlation. ❑Understand correlation coefficient. ❑Enumerate the features of correlation. ❑Familiarize oneself with the correlation formula. ❑Define Simple Linear Regression and enumerate its observed patterns. ❑Familiarize oneself with the regression formula. The Country’s 1st Polytechnic U Correlation and Linear Regression Correlation is a statistical term describing the process of establishing the relationship or connection between two different variables or measures. The Country’s 1st Polytechnic U Correlation and Linear Regression Time spent on watching TV Examination Scores The Country’s 1st Polytechnic U Correlation and Linear Regression Advertising expenses Revenue The Country’s 1st Polytechnic U Correlation and Linear Regression Amount of fertilizer Crop yields The Country’s 1st Polytechnic U Correlation and Linear Regression Training regimen Athletes' performance The Country’s 1st Polytechnic U Correlation and Linear Regression Time Population growth The Country’s 1st Polytechnic U Correlation and Linear Regression Education or experience Salary The Country’s 1st Polytechnic U Correlation and Linear Regression Number of student absences Scores in exams The Country’s 1st Polytechnic U Correlation and Linear Regression Age Eye glasses The Country’s 1st Polytechnic U Correlation and Linear Regression Height Weight The Country’s 1st Polytechnic U Correlation and Linear Regression Income Expenses The Country’s 1st Polytechnic U Correlation and Linear Regression Temperature Ice Cream Sales The Country’s 1st Polytechnic U Correlation and Linear Regression High-cost Apartment Apartment Sales The Country’s 1st Polytechnic U Correlation and Linear Regression A correlation coefficient is a number that describes how close to a linear relationship there is between two variables or measures. The Country’s 1st Polytechnic U Correlation and Linear Regression Where: n = number of data pairs Σx = the sum of the X values Σy = the sum of the Y values Σxy = the sum of the product of x and y values Σx^2 = the sum of the squares of the x values Σy^2 = the sum of the squares of the y values The Country’s 1st Polytechnic U Correlation and Linear Regression Regression analysis is a mathematical measure of the average relationship between two or more variables in terms of original units of data. The statistical tool with the help of which we can estimate (or predict) the unknown values of one variable from known values of another variable is called regression. With the help of regression analysis, we can find out the average probable change in one variable given a certain amount of change in another. Regression analysis is thus designed to examine the relationship of variable y to variable x. The Country’s 1st Polytechnic U Correlation and Linear Regression Features of Linear Regression ❑ The objective of regression analysis is to study the ‘nature of the relationship’ between the variables so that we may be able to predict the value of one based on another. ❑ The cause-and-effect relation is clearly indicated through regression analysis – one variable is taken as dependent and the other as an independent. ❑ The variable whose value is influenced is called the dependent variable and is denoted by y; the variable that exerts the influence is called the independent variable and is denoted by x. The Country’s 1st Polytechnic U Correlation and Linear Regression Analyzing a Scatterplot Positive Relationship Negative Relationship Nonlinear Relationship No Relationship The Country’s 1st Polytechnic U Correlation and Linear Regression Analyzing a Scatterplot ❑ A positive relationship exists when the point falls approximately in an ascending straight line from left to right, where the X and Y values increase at the same time. ❑ A negative relationship exists when the point falls approximately in a descending straight line from left to right, where the X and Y values decrease at the same time. ❑ A nonlinear relationship when the points fall in a curve line. ❑ A no relationship exists when there is no discernible pattern to the points. The Country’s 1st Polytechnic U Correlation and Linear Regression Example: Pharmex is a chain of drugstores that operates around the country. To see how effective its advertising and other promotional activities are, the company has collected data from 50 randomly selected metropolitan regions. In each region it has compared its own promotional expenditures and sales to those of the leading competitor in the region over the past year. There are two variables: Promote: Pharmex’s promotional expenditures as a percentage of those of the leading competitor Sales: Pharmex’s sales as a percentage of those of the leading competitor The Country’s 1st Polytechnic U Correlation and Linear Regression The Country’s 1st Polytechnic U Correlation and Linear Regression Objective To use a scatterplot to examine the relationship between promotional expenses and sales at Pharmex. Solution It is customary to put the explanatory variable on the horizontal axis and the dependent variable on the vertical axis. In this example the store believes large promotional expenditures tend to “cause” larger values of sales, so Sales is on the vertical axis and Promote is on the horizontal axis. The Country’s 1st Polytechnic U Correlation and Linear Regression The Country’s 1st Polytechnic U Correlation and Linear Regression Linear Regression Formula: Y = a + bX Where: Y = dependent variable a = intercept (the value of Y when X = 0) b = slope X = independent variable The Country’s 1st Polytechnic U Correlation and Linear Regression The Country’s 1st Polytechnic U Correlation and Linear Regression Example Problem: Is there a relationship between the number of hours spent by BSBA students studying and their scores in the Midterm Examination? Student 01 02 03 04 05 06 07 08 09 10 Hours 4 3 2 3 2 1 4 4 1 3 Scores 13 13 9 12 10 10 14 15 9 12 The Country’s 1st Polytechnic U Correlation and Linear Regression QUESTIONS? CLARIFICATION? The Country’s 1st Polytechnic U