Correlation

Data Analytics and Economics LECTURE Section: 2E-3 (ECO5103) Schedule: Saturday (10:00am – 12:00pm)

PEARSON R CORRELATION AND MULTIPLE CORRELATION

Correlation? üThe analysis or assessment that deals with association between two or more variables. Positive and Negative Positive and Type I Negative Correlations Linear and Non-Linear Association Show us how to determine both the Linear and Type II nature and strength of relationship Non-Linear between variables The measurement of correlation is also Simple and Multiple Type III called “Correlation Coefficient”

Correlation ( -1 ≤ r ≥ +1) -1 ü The measure of correlation Strong called the correlation Negative Relationship coefficient, (r) ü The degree of relationship Strong is expressed by coefficient Positive which range from Relationship +1

TYPE I Positive If the values of two variables Correlation changing direction. Variables change in Negative the same direction. Correlation Values of variables change Zero Correlation If both the variables are Opposite independent Directions No change

TYPE I, II, and III ü The basis of the correlation is based form the parameters that will be set. ü The result cannot be manipulated unless the data will be tampered or change. ü In addition, if the data will be manipulated, it will result to ”Non- Linear, No Correlation, or Negative Correlation.” ü Type III, is the aggregated data from the set of variables available.

Pearson R Correlation § The Correlation Coefficient: A single summary number that tells you whether a relationship exists between two variables, how strong that relationship is and whether the relationship is positive or negative. § The Coefficient of Determination: A single summary number that tells you how much variation in one variable is directly related to variation in another variable.

Why does a person receive the compensation that they do? How long a person has worked Type of work they do? for the company? Their Age What part of the country (Age is a “proxy” for experience). they live in? How much experience a person has doing their specific kind of work? Performance Rating?

Relationship between Age and Current Compensation tVhaartiahtaiosnnionthCinogmtopedno swaittihoangse Age Compensation ASSUMPTION: Variation of Age that has nothing Variance accounted by the § In this example, 27% of what there is to know to do with compensation relationship between age and about a person’s current compensation is accounted for by that person’s age. compensation § In other words, if you know a person’s age, you know about 27% of what you need to know to make an accurate prediction about what their compensation is.

Relationship between Age, Time with Company and Compensation 10% of why a person earns what they do is related Time with the company Age Compensation Notice that a person’s time with company accounts for about 10% of why they earn what Time with they do. By adding this variable to our study, the Company we improved our understanding of why people earn the income they do from 27% to 37%. In 27% of why a person earns what other words, using two variables rather than one they do is related to person’s age. variable, we improved our ability to make accurate predictions about a person’s salary do is related to person’s age.

11% of the variation College Degree 45% of why a person earns what they do shared by college is related to college degree but is degree and age is Compensation unrelated to age unrelated to income Notice that this is much more complicated! Age 12% of a person’s compensation is related to age, 45% is related to a person’s college 12% of why a person earns in terms of a degree and 20% is related to an interaction person’s age, but is unrelated to what they between age and college degree. In this do is related to the person’s college degree case we have pumped up our ability to predict/explain compensation to nearly 88%! 20% of income is related to an “Interaction” of age and college degree

How to compute ‘r’ (Correlation and Multiple Coefficient) SCENARIOS: 1. You went out and took a random sample of 5 currently employed General Let’s assume that you are a Motors salespeople. personnel psychologist working for 2. You collected the following information about each of the 5 salespeople: General Motors. The company want to develop a new hiring process § Years of School Completed that will help them identify job § Motivation as measured by the Higgins Motivation Scale applicants who will be the most productive car salespeople. § How many dollars in sales the person made last year 3. You calculate the correlation between each possible pair of variables 4. Plug the correlations into the Multiple r formula (If you will use SPSS) 5. Do the math!

Simulate result of “r” (Correlation and Multiple Coefficient) SPSS Simulation the Correlation of the following: § Year of School Completed with Motivation § Years of School Completed with Dollars in Sales § Motivation with Dollars in Sales

Parameters to be used Decision Rule: ü >.05 Accept HO (Not Significant) ü < .05 Reject HO (Significant) If…. Decision on HO Interpretation >0.05 <0.05 Accept Not Significant Reject Significant

Hypothesis Assumptions Ho : There is no significant relationship between “Years of School Completed, Higgins Motivational Scale towards the Annuals Sales. HSc1ho: oTl hCeorempilsetesdig, nHifiicgagnints relationship between “Years of Annuals Sales. Motivational Scale towards the

STEP 1 – Select your Random Sample STEP 2 – Collect your Data TABLE 1: Data Collected From Random Sample of 5 General Motors Salespeople Independent Variable 1 (X1) Independent Variable 2 (X2) Dependent Variable (Y) HIGHEST YEAR OF MOTIVATON AS MEASURED BY ANNUAL SALES SCHOOL COMPLETED HIGGINS MOTIVATIONAL SCALE (IN DOLLARS) 12 32 350,000 14 35 399,765 15 45 429,000 16 50 435,000 18 65 433,000

Determination of Strength of Association Pearson R Correlation

Step 1: Strength of association between Highest Year School Completed and Motivation Predictors Pearson Sig. Decision on HO Interpretation Significant Highest Year School Completed Correlation (2-Tailed) Higgins Motivational Scale .968** .007 Reject *. Correlation is significant at the 0.05, **. Correlation is significant at the 0.01 Decision Rule for assessing if the test is significant (for α=.05): If p≤.05 (There is a significant relationship), if p≥.05 (There is no significant relationship) The table shows the correlation coefficient between the “Highest Year School Completed and Higgins Motivational Scale”. It can be seen in the coefficient indicating that “There is a positive strong” significant relationship with a Pearson Correlation value of 0.968” equivalent to 96.8%. The result suggest, we can predict that there is a 96.8%, that highest year school completed is associated towards the Motivation Scale of the employees.

Step 2: Strength of association between Highest Year School Completed and Higgins Motivational Scale Predictors R2 Linear 0.937 Highest Year School Completed Higgins Motivational Scale The R2 linear value of 0.937 which is equivalent to 93.7% of changing variation. Which is represented by the Highest Year School Completed Average towards its Higgins Motivational Scale.

Step 3: Interpretation and Analysis : Strength of association between Highest Year School Completed and Higgins Motivational Scale Predictors p-value (2-tailed) Highest Year School Completed Higgins Motivational Scale .007 Therefore, we can conclude that 95% the Highest Year School Completed and Higgins Motivational Scale, that 0.025 0.025 there is enough evidence based on the result of the simulation that we can suggest that the indicators have a significant correlation with a p-value of .007 or 99.3% confidence level.

Step 3: Interpretation and Analysis : Strength of association between Highest Year School Completed and Higgins Motivational Scale Predictors p-value 95% (1-tailed) Highest Year School Completed 0.05 Higgins Motivational Scale .003 Therefore, we can conclude that the Highest Year 95% School Completed and Higgins Motivational Scale, that there is enough evidence based on the result of the 0.05 simulation that we can suggest that the indicators have a significant correlation with a p-value of .003 or 99.7% confidence level.

Strength of association between Highest Year School Completed and Annual Sales Predictors Pearson Sig. Decision on HO Interpretation Significant Highest Year School Completed Correlation (2-Tailed) Annual Sales .880** .049 Reject *. Correlation is significant at the 0.05, **. Correlation is significant at the 0.01 Decision Rule for assessing if the test is significant (for α=.05): If p≤.05 (There is a significant relationship), if p≥.05 (There is no significant relationship) The table shows the correlation coefficient between the “Highest Year School Completed and Annual Sales”. It can be seen in the coefficient indicating that “There is a positive strong” significant relationship with a Pearson Correlation value of 0.880” equivalent to 88.0%. The result suggest, we can predict that there is an 88.0%, that highest year school completed is associated towards the annual sales of the employees.

Strength of association between Highest Year School Completed and Annual Sales Predictors R2 Linear 0.774 Highest Year School Completed Annual Sales The R2 linear value of 0.774 which is equivalent to 77.4% of changing variation. Which is represented by the Highest Year School Completed Average towards its Annual Sales.

Interpretation and Analysis : Strength of association between Highest Year School Completed and Annual Sales Predictors p-value .049 Highest Year School Completed Annual Sales Therefore, we can conclude that the Highest Year School Completed and Annual Sales that there is enough evidence based on the result of the simulation that we can suggest that the indicators have a significant correlation with a 95.1% confidence level.

Strength of association between Annual Sales and Higgins Motivational Scale Predictors Pearson Sig. Decision on HO Interpretation Not Significant Annuals Sales Correlation (2-Tailed) Higgins Motivational Scale .772** .126 Accept *. Correlation is significant at the 0.05, **. Correlation is significant at the 0.01 Decision Rule for assessing if the test is significant (for α=.05): If p≤.05 (There is a significant relationship), if p≥.05 (There is no significant relationship) The table shows the correlation coefficient between the “Annual Sales and Higgins Motivational Scale”. It can be seen in the coefficient indicating that “There is a positive strong” significant relationship with a Pearson Correlation value of 0.772” equivalent to 77.2%. The result suggest, we can predict that there is an 77.2%, that Annual Sales is associated towards the Motivation Scale of the employees

Strength of association between Higgins Motivational Scale and Annual Sales Predictors R2 Linear 0.596 Annuals Sales Higgins Motivational Scale The R2 linear value of 0.596 which is equivalent to 59.6% of changing variation. Which is represented by the Annual Sales towards its Higgins Motivational Scales.

Interpretation and Analysis : Strength of association between Annual Sales and Higgins Motivational Scale Predictors p-value .126 Highest Year School Completed Annual Sales Therefore, we can conclude that the Annuals Sales Completed and Higgins Motivational Scales that there is enough evidence based on the result of the simulation that we can suggest that the indicators have no significant correlation with an 87.4% confidence level.

Hypothesis Decisions Predictors Pearson P-value Decision Interpretation Correlation on HO Year of School Completed with Motivation .007 Reject Significant Years of School Completed with Dollars in Sales .968** .049 Significant Motivation with Dollars in Sales .126 Reject Not Significant .880** Accept .772** *. Correlation is significant at the 0.05, **. Correlation is significant at the 0.01 Decision Rule for assessing if the test is significant (for α=.05): If p≤.05 (There is a significant relationship), if p≥.05 (There is no significant relationship) Ho : There is no significant relationship between What business decisions to take “Years of School Completed, Higgins Motivational into considerations? Scale towards the Annuals Sales. H1 : There is significant relationship between “Years of School Completed, Higgins Motivational Scale towards the Annuals Sales.

Econometric Model: INDEPENDENT VARIABLE (X1) Solow’s Growth Model Population Growth Dependent Variable INDEPENDENT VARIABLE (X2) (Y) Unemployment Rate Real Gross Domestic INDEPENDENT VARIABLE (X3) Product Labor Force Growth Rate THE ROLE OF POPULATION TOWARDS ECONOMIC GROWTH IN THE PHILIPPINES

How to compute ‘R’ (Correlation and Multiple Coefficient) SCENARIOS: 1. You collected the following data from sources: Let’s assume that we want to § Population measure the implication of § Unemployment Rate Population towards Economic Growth § Labor Force § Real GDP 2. You calculate the correlation between each possible pair of variables 3. Plug the correlations into the Multiple R formula (If you will use SPSS) 4. Do the math!

Simulate result of “r” (Correlation and Multiple Coefficient) Simulation the Correlation of the following: § Economic Growth to Population Growth § Economic Growth to Unemployment Rate § Economic Growth to Labor Force Growth Rate

Parameters to be used If…. Decision on HO Interpretation >0.05 Accept Not Significant <0.05 Reject Significant Decision Rule: ü .05 Accept HO (Not Significant) ü < .05 Reject HO (Significant) Hypothesis Assumptions Ho : There is no significant relationship between “Economic Growth towards Population, Unemployment, and Labor Force. H1 : There is significant relationship between “Economic Growth towards Population, Unemployment, and Labor Force.

STEP 1 – Sources of Data Sample STEP 2 – Collect your Data TABLE 1: Data Collected from World Bank Independent Variable Independent Variable 2 Independent Variable 3 Dependent Variable Year (X1) (X2) (X3) (Y) Real GDP Population Unemployment Labor Force Growth Growth Rate (%) Rate 1 61,895,160 8.10 3.01 5267 2 63,454,786 10.60 2.85 5237 3 65,020,116 9.90 2.9 5255 9.30 2.92 5366 4 66,593,904 9.50 2.88 5601 5 68,180,859 …. …. … … 30 ………

Determination of Strength of Association Pearson R Correlation

Step 1: Strength of association between Economic Growth and Population Predictors Pearson Sig. Decision on HO Interpretation Not Significant Real Gross Domestic Product Correlation (2-Tailed) Population Growth .834** .079 Accept *. Correlation is significant at the 0.05, **. Correlation is significant at the 0.01 Decision Rule for assessing if the test is significant (for α=.05): If p≤.05 (There is a significant relationship), if p≥.05 (There is no significant relationship) The table shows the correlation coefficient between the “Real GDP and Population Growth”. It can be seen in the coefficient indicating that “There is a positive strong” significant relationship with a Pearson Correlation value of 0.834” equivalent to 83.4 %.

Step 2: Strength of association between Economic Growth and Population Predictors R2 Linear 0.695 Real Gross Domestic Product Population Growth The r2 linear value of 0.695 which is equivalent to 69.5% of changing variation. This is represented by the Population Growth towards its Real Gross Domestic Product

Step 3: Interpretation and Analysis : Strength of association between Economic Growth and Population Predictors p-value (2-tailed) Real Gross Domestic Product Population Growth .079 Therefore, we can conclude that 95% the Population and Real GDP, that 92.1% there is enough evidence based on the result of the simulation that we can 0.025 0.025 suggest that the indicators have NO significant correlation with a p-value of .079 or 92.1% confidence level.

End of Session Thank you!

Way forward ü Regression (Simple and Multiple) ü Assessment Activities (Validation Assessment #2) ü 2 Attempts (Highest Score shall be recorded) ü Maximum of 90 Minutes ü Minimum of 20 items (Multiple Choice, Identification, True or False, Evaluation, and computation) ü 1 week to complete Details shall be uploaded to our FB Group