Correlation Analysis Material

SUMMARY OF CORRELATION ANALYSIS MATERIAL STATISTICS COURSE 1. What is meant by correlation analysis? Answer : Correlation analysis is a form of analysis used to determine the direction of the relationship between two or more variables (Siregar: 2017; Gunawan: 2016). And also to find out the magnitude of the influence caused by one variable (independent variable) on other variables (dependent variable). If viewed from the direction, the relationship between variables is divided into 3 relationships, state and explain them with examples of the types of relationships between variables Answer : If viewed from the direction of the relationship between two or more variables, there are 3 types of relationship, namely: 1. Unidirectional relationship Namely when the relationship between two or more variables is the same or in the same direction. If variable X experiences an increase, then variable Y will also experience an increase and vice versa. For example, if the price of palm oil increases, the price of cooking oil will also increase and vice versa. 2. The relationship is in the opposite direction The relationship between two or more variables is not unidirectional. If variable X decreases, then variable Y increases. For example, when someone always practices doing math problems, the level of difficulty in doing math problems will decrease. 3. Reciprocal relationship Is a relationship between two or more variables that influence each other. For example, when someone exercises diligently, it will have an effect on their body's health. 2. Explain with examples the types of relationships between variables! Answer : Judging from the form of relationship between variables, there are 3 types of relationship, namely: 1. Symmetrical relationship A relationship that states the nature of togetherness between two or more variables, but does not show a causal relationship or mutual influence. In this form of relationship it is not known with certainty which is the independent variable and the dependent variable because the two variables do not influence each other. For example: the relationship between expensive clothing and appearance, the relationship between crows and someone's death. 2. Causal relationship A causal relationship between two or more variables that influence one variable and another variable. In this form, independent variables and dependent variables can be distinguished. For example: the relationship between education level and a person's work ability. 3. Interactive relationships The relationship between two or more variables that influence each other where the positions of the variables x and y alternate. For example, the relationship between work motivation (influencing) and work performance (influencing) 3. Explain the difference between correlation coefficient and determination coefficient Correlation coefficient Determination Coefficient 2 2 R R2 Amount variable Symbol Formula Rxy = ∑𝑥𝑦 Kd: r2.100% √(∑𝑥2𝑦2) Information: Information : Kd = Coefficient of Rxy : Correlation between x determination or how far the variabel and yX : Xi – 𝑋 dependent variable changes ( Y : Yi – 𝑦 Audit Quality) 4. Name 3 analytical tools used to analyze correlation, give case examples of each analytical tool Answer : 1. Pearson product moment correlation analysis tool Used if both variables have a numerical scale (both ratios or intervals or a mixture of ratios and intervals). Pearson correlation is suitable for parametric statistics. When the data is large and has parameter measures such as the mean and standard deviation of the population. An example of this is looking for the correlation coefficient between the mathematics scores obtained by students. To find out the relationship between the rupiah exchange rate and changes in the IHSG. For example, the data collected is daily data for 100 days. 2. Spearmen rank analysis tool Used if one of the two variables has a numerical scale (ratio or interval), then the other variable has at least an ordinal scale. The Spearman Rank correlation coefficient is more suitable for use in nonparametric statistics and data with small samples. For example, two judges assess eight competition participants. To determine the relationship between the level of education and the level of public awareness of government policies 3. Point- serial correlation analysis tool Used to calculate the correlation between two variables, one on a nominal scale and the other on an interval scale. For example, the correlation between gender (nominal symptom) and mathematical ability (interval symptom). 5. Answer case 2 contained in the 12th meeting material Case 2 A company wants to see the relationship between the duration of advertisements for product X broadcast per month by one of the private television stations and its sales level. Then, the duration of the ad display and the sales level for each month are taken a year, with the following data: Months Period Duration (In Sales of Goods (Per Unit) Minutes) January 45 35240 February 55 36540 March 40 35000 April 60 42500 May 70 43000 June 60 42500 July 50 37500 August 45 40000 September 35 32000 November 55 41500 October 65 42500 December 60 43000 Question 1. How big is the relationship (correlation) between the duration variable and the goods sales variable? Answer : The magnitude of the relationship between the duration variable and the goods sales variable is 0.878, which shows that the correlation relationship is very strong and in the same direction (positive). 2. How big is the contribution/contribution of the duration variable to the goods sales variable? Answer : The contribution or variable contribution to sales of goods is 77.1% and the remaining 22.9% is influenced by other factors. Steps Answer case 2 questions above using the Pearson Product Moment analysis tool Data (n) Duration (x) Selling (y) xy X2 Y2 1 45 35.240 1.585.800 2.025 1.241.857.600 2 55 36.540 2.009.700 3.025 1.335.171.600 3 40 35.000 1.400.000 1.600 1.225.000.000 4 60 42.500 2.550.000 3.600 1.806.250.000 5 70 43.000 3.010.000 4.900 1.849.000.000 6 60 42.500 2.550.000 3.600 1.806.250.000 7 50 37.500 1.875.000 2.500 1.406.250.000 8 45 40.000 1.800.000 2.025 1.600.000.000 9 35 32.000 1.120.000 1.225 1.024.000.000 10 55 41.500 2.282.500 3.025 1.722.250.000 11 65 42.500 2.762.500 4.225 1.806.250.000 12 60 43.000 2.580.000 3.600 1.849.000.000 Total 640 471.280 25.525.500 35.350 18.671.279.200 The Pearson Product Moment correlation coefficient formula is as follows: 12 (25.525.500)−(640)(471.280) Rxy = √{12(35.350)−(640)2}{12(18.671.279.200)−(471.280)2} 306.306.000−301.619.200 Rxy = √{424.200−409.600}{224.055.350.400−222.104.838.400} 4.686.800 Rxy = √{14.600}{1.950.512.000} Rxy = 4.686.800 5.336.429,06 Rxy = 0.878 (korelasi sangat kuat) R2 = (0,878)2 = 0,771 KD = 0,771 X 100% = 77,1 % From the calculation results above, it can be concluded that there is a relationship between the duration variable and the goods sales variable of 0.878, which shows a very strong and unidirectional (positive) correlation relationship. The contribution or variable contribution to sales of goods is 77.1% and the remaining 22.9% is influenced by other factors.