Independent variable (x) • Also called predictor or explanatory or manipulated variable • the variable in regression that can be controlled or manipulated Dependent variable (y) • Also called the response variable • the variable that cannot be controlled or manipulated 7 uitm. edu. my uitm. edu. my 8 Dependent(x) Vs. Independent(y) • • • • Intentionally manipulated Controlled Vary at known rate Cause • • • • Intentionally left alone Measured Vary at unknown rate Effect Example: What affects a student’s arrival to class? Variables: • Type of School ? FSPPP, Business School, FSKM Type of Student ? Gender? CGPA? • Class Time ? Morning, Afternoon, Evening • Mode of Transportation ? Motorcycle, Car, UiTM bus 2 QMT412 Pn. Sanizah’s Notes 02/05/2013 9 uitm. edu. my uitm. edu. my 10 scatter plot (scatter diagram) • A scatter plot is used to show the relationship between two variables. • The scatter plot is a visual way to describe the nature of the relationship between the independent variable (x) and the dependent variable (y).
• Interpreting scatter plots: ? ? ? ? Positive linear relationship Negative linear relationship Nonlinear relationship No relationship
Scatter Plot Examples Linear relationships y y Nonlinear (Curvilinear) relationships Positive x y x y x Negative x 11 uitm. edu. my uitm. edu. my 12 Scatter Plot Examples Strong relationships y y (continued) Weak relationships Scatter Plot Examples No relationship y (continued) x y y x y x x x x 3 QMT412 Pn. Sanizah’s Notes 02/05/2013 13 14 Example 1 (pg. 134) x 1 3 5 7 9 uitm. edu. my correlation coefficient uitm. edu. my • Draw a scatter diagram for the following data and state the type of relationship between the variables. 13 17
The Review on Public Perception Towards Intercultural Romantic Relationship Based On Yasmin Ahmad Movie " Sepet"
PUBLIC PERCEPTION TOWADS INTERCULTURAL ROMANTIC RELATIONSHIP BASED ON YASMIN AHMAD MOVIE “SEPET” CHAPTER 1: INTRODUCTION 3 1.1 Background of Study 3 1.2Problem Statement 5 1.3Research Objectives 6 1.4Scope and Rationale of Study 7 1.5Significance of Study 8 1.6Profile 9 CHAPTER 2: LITERATURE REVIEW 10 CHAPTER 3:RESEARCH METHODOLOGY 14 3.1 Background (Qualitative Paradigm) 15 3.2Population ...
Correlation coefficient measures the strength and direction of a LINEAR relationship between a pair of random variables. y 0 5 11 14 19 22 30 The POPULATION correlation coefficient ? (rho) measures the strength of the association between the variables. The sample correlation coefficient r or ? s is an estimate of ? and is used to measure the strength of the linear relationship in the sample observations. 15 uitm. edu. my uitm. edu. my 16 Correlation Coefficient • “r” or “? s” indicates… ? strength of relationship (strong, weak, or none) ? direction of relationship ? ositive (direct) – variables move in same direction ? negative (inverse) – variables move in opposite directions • r ranges in value from –1. 0 to +1. 0. Moderate Weak Weak Moderate Do Variables Relate to One Another? Is teacher’s pay related to performance? Is exercise related to illness? Is CO2 related to global warming? Is TV viewing related to shoe size? Is shoe size related to height? Is height related to IQ? Is cigarettes smoked per day related to lung capacity? Positive Negative Positive Zero Negative -1. 0 -ve Perfect Positive -0. 8 -0. 5 0. 0 No Relationship +0. 5 +0. 8 +1. 0 +ve Perfect Very Strong Strong
Strong Very Strong 4 QMT412 Pn. Sanizah’s Notes 02/05/2013 17 uitm. edu. my uitm. edu. my 18 Positive correlation Two variables move in the same direction Negative correlation Two variables tend to go in the opposite direction 19 uitm. edu. my Pearson Coefficient of Correlation • Both variables must be quantitative and normally distributed. • Calculation for r : r? Methods for Calculating Correlation Coefficient, r or ? s ?n ? ? ? xy ? ? x? y 2 2 ? x ? ?? x ? ? ? n? y 2 ? ?? y ? ? ? ? ? ? ? ? n 2 Pearson ProductMoment Correlation Coefficient Spearman rank correlation Coefficient or r? xy ? ?n ? ? x ? 2 ? ? y 2 ? ?? y ? 2 ? ?? x 2 ? ? ? ? ? ? n ? ?? n ? xy ? ? ? ? uitm. edu. my 20 5 QMT412 Pn. Sanizah’s Notes 02/05/2013 Example 2 • Refer to Example 1. Compute Pearson coefficient of correlation and interpret the result. The Spearman rank correlation coefficient • Spearman’s rank correlation coefficient is a measure of association between two variables that are at least of ordinal scale (suitable for qualitative data).
The Research paper on Pearson's Product – Moment Correlation Coefficient
The r value for the relationship between Hamstring strength index 60o and the Shuttle run test is -0.149. This r value shows a weak correlation between the two variables, as it is less than the 0.3 threshold for significance. Therefore, the r value is not significant. Question 2 Between r=1.00 and r=-1.00, there is no difference in terms of strength. Both values are on the extreme ends of the ...
• Can also be applied to quantitative data but the variables must firsts be ranked and then only it is calculated based on these rankings. ? x ? ________ ? x 2 ? ________ ? ? ________ ? y 2 ? ________ ? xy ? ________ n ? ________ r? ? xy ? ?n ? ? x ? 2 ? ? ? y ? 2 ? ?? x 2 ? ? ? ?? y 2 ? ? ? ? n ? ? n ? xy ? ? ? ? ?s ? 1 ? 6? d 2 n ( n 2 ? 1) where: d = difference between two ranks n = number of pairs of observations uitm. edu. my NOTE: Be careful with tied observations uitm. edu. my 21 22 23 24 uitm. edu. my How to calculate Spearman’s rank correlation coefficient? 1. 2. 3. 4. uitm. edu. my Refer Example 5 pg. 140 Five students A, B, C, D, E are ranked in two subjects, statistics and computer programming with the following results.
Calculate the Spearman’s rank correlation coefficient. Subject Student Statistics Computer List each set of scores in a column. Rank the two sets of scores. Place the appropriate rank beside each score. Head a column d and determine the difference in rank for each pair of scores. (Note: Sum of the d column should always be 0) 5. Square each number in the d column and sum the values (? d 2).
6. Use the formula to calculate the correlation coefficient. d d2 ?s ? 1 ? 6? d 2 n ( n 2 ? 1) A B C D E 1 2 3 4 5 3 1 4 2 5 6 QMT412 Pn. Sanizah’s Notes 02/05/2013 25 26 Refer Example 6 pg. 141 x y uitm. edu. my The Regression Line d2 uitm. edu. my Rank of x, Rank of y, Rx Ry d=Rx-Ry 6. 0 6. 2 6. 5 6. 8 7. 0 7. 2 7. 5 7. 8 8. 0 8. 2 8. 4 8. 7 80 80 78 75 70 60 60 55 50 48 45 40 ? Regression indicates the degree to which the variation in one variable X, is related to or can be explained by the variation in another variable Y ? Once you know there is a significant linear correlation, you can write an equation describing the relationship between the x and y variables. ? This equation is called the line of regression or least squares line. • The equation of a line may be written as: y ? a ? bx • where b is the slope of the line and a is the y-intercept.
The Essay on Costs and Total Variable Cost
Explain in a nontechnical way why demand iselastic in the northwest segment of the demand curve and inelastic in the southeast segment. Product PriceQuality Demanded $51 Vb 42 33 24 15 Answer: 1/1. 5 / ?. 5= . 67%/ 22%= 3. 05 Ch 22 #7 1. Key Question A firm has fixed costs of $60 and variable costs as indicated in the table on the following page. Complete the table and check your calculations by ...
