Summary of Regression Analysis Material

SUMMARY OF REGRESSION ANALYSIS MATERIAL STATISTICS COURSE 1. What is meant by regression analysis? Answer : Regression analysis is a causality analysis. Regression analysis is an analytical tool used to predict future conditions based on past data. And it is also used to describe the functional relationship between two variables. 2. What is the difference between simple regression analysis and multiple regression analysis? Answer : Simple linear regression analysis is a regression analysis that only involves two variables, namely 1 (one) dependent variable or dependent variable and 1 (one) independent or independent variable. Meanwhile, multiple linear regression analysis is a regression analysis that involves more than two variables, namely 1 (one) dependent variable or dependent variable and more than 1 (one) independent or independent variable. 3. In regression analysis, data is grouped into 2, namely dependent variables and independent variables. What are meant by these 2 types of variables? Answer : a. Independent variables are variables that influence or cause changes in the emergence of the dependent variable. b. Dependent variables are variables that are influenced, as a result of the existence of independent variables. It is said to be a dependent variable because the dependent variable is influenced by the independent variable (independent variable). 4. Before carrying out regression analysis, research data must be tested using the classic assumption test, explain what is meant by the six assumptions in this classic test! Then look for the differences between the six tests in a matrix like the following! Fungtion Equipment Test Test Criteria Normality To assess the 1. Chi Square 1. Data is arranged in groups or Test distribution of data Method grouped in a group of data or (Normal distribution table. variables, whether Distribution the data distribution Goodness of is normally fit Test) distributed or not. in a frequency 2. Suitable for data with large numbers (n>30). 2. Lilliefors method 3. Kolmogorov 3. Each cell must be filled, which is less than 5 combined Smirniov Method Homogenity To find out whether Bartlett's Test Homogeneity criteria are Test the data in variables Harley Pearson's determined if the value: calculated X and Y are Test Chi-Square < table Chi-Square. homogeneous or not. Homogeneity of variance test Linearity Test To see Durbin- Watson 1. These two variables are whether the model test, Ramsey test said to be linear if the built has a linear or test significance is more than relationship or not. Lagrange 0.05 so that decision Multipliers making takes the form of a linear relationship. Meanwhile, if the significance is below 0.05 then the decision making takes the form of no linear relationship between the two variables. 2. Looking at the F calculated and F table values, if F calculated > F table then the conclusion is that there is no linear relationship between the two variables, whereas if F calculated < F table then the conclusion is that there is a linear relationship between the two variables. Auto correlation To see Durbin- Test does it happen? Watson Watson) < dL or > correlation Test, Test (4-dL) then Ho is 1. If d between a period with Run rejected, t means and the Test and if previous period the (t - 1). observatio (Durbin which there is autocorrelation. 2. If d lies between n data is dU and (4- dU) above 100 then data it is accepted, best to use means there is no the autocorrelation. Ho is which Lagrange 3. If d lies between Multiplier dL and dU or test between (4- dU) and (4-dL), then it does not produce a definite conclusion. 1. If the VIF value is Multicollinearity . To determine test whether there is a inflation <10.00, it means correlation factor (VIF), that there is no high between Pearson multicollinearity independent correlation in the regression variables in between model. multiple linear independent regression variables, or Variance 2. If the VIF value is models. If there is by looking at > 10.00, it means a high correlation eigenvalues that between and condition multicollinearity independent index (CI). occurs in the variables The relationship between the regression model. independent variable and the dependent variable is disturbed. Test Heteroscedasticity To find out if Test there are Glejser symptoms of Test Park heteroscedasticity. irregularities from 1. Ho: there are no 2. Ha: there are the requirements for Spearman's test classical symptoms of heteroscedasticit 3. Ho is accepted if in Viewin linear regression, g Charts the significance is where there is no assumptions the > 0.05, meaning regression model heteroscedasticity must fulfill the and Ho is rejected condition of the if the significance absence is < 0.05, which of heteroscedasticit means there is y. heteroscedasticity. 1. Complete case 4 in the material to make conclusions and interpretations! A survey conducted in Maju Makmur village was used to determine the functional relationship between land area (hectares) and price (millions of rupiah). If paired data on land area and price are obtained, what is the functional relationship? Hipotesis : Ho : Land area has no effect on land prices Ha : Land area has an effect on land prices 1. Significance Level :  : 5% 2. Testing Rules : If Ttable  Tcount  ttable, then Ho accepted If TCount > Ttable, then Ho rejected Wide 0.75 0.55 1.00 1.25 2.50 3.00 4.50 3.75 5.00 3.25 3.25 2.75 2.75 2.00 4.00 Price 2.45 2.20 2.80 3.60 5.80 7.40 9.00 8.50 10.00 8.00 7.50 6.00 6.25 4.00 8.00 3. Calculate the constant value and intercept value n Wide (X) Price (Y) XY X2 1 0.75 2.45 1.84 0.56 2 0.55 2.20 1.21 0.30 3 1.00 2.80 2.80 1.00 4 1.25 3.60 4.50 1.56 5 2.50 5.80 14.50 6.25 6 3.00 7.40 22.20 9.00 7 4.50 9.00 40.50 20.25 8 3.75 8.50 31.88 14.06 9 5.00 10.00 50.00 25.00 10 3.25 8.00 26.00 10.56 11 3.25 7.50 24.38 10.56 12 2.75 6.00 16.50 7.56 13 2.75 6.25 17.19 7.56 14 2.00 4.00 8.00 4.00 15 4.00 8.00 32.00 16.00 Total 40.30 91.50 293.49 134.24 Konstanta b b = Intersept a 𝑛.Σ𝑥𝑦− Σ𝑥Σ𝑦 a = 𝑛.Σ𝑥2−(Σ2) = Σ𝑌−𝑏.Σ𝑋 𝑛 15 (293.485)−40.3(91.5) = 91.5−1.835 (40.3) 15 15(134.24)−(40.3)2 = 4,402.275−3,687.45 = 17.5495 15 2,013.6−1,624.09 = 714.825 389.51 = 1.835 = 1.169 4. Create regression equations and interpretation Regression equation Yi = a + bXi Yi = 1.169 + 1.835Xi Interpretation If X = 0 Then Y = 1.169 If X =1/plus one, then Y=3.004 So, if the land area is (X=0), then it is estimated that the land price will be sold for 1,167 million rupiah. However, if the land area increases by 1 hectare (X=1), it is estimated that the land price will be sold for 3,004 million rupiah.. 5. Test significance by calculating the t count ANOVA df SS MS 1 87.45599696 87.456 Residual 13 2.999003042 0.230693 Total 14 90.455 Regression F count is 379,102 with a significance value of 5,327 F Significance F 379.102 5.32717E-11 6. Compare T count with T table ANOVA df SS MS 1 87.45599696 87.456 Residual 13 2.999003042 0.230693 Total 14 90.455 Regression F Significance F 379.102 5.32717E-11 Significance value = 5.32717E-11 So, significance value > alpha = 0.05 or 5% So it can be concluded that if t count > t table, then Ho is rejected. Make decision Based on the results of comparing tcount with ttable, the result Ho is rejected. This means that, with a significance level of 5%, it can be concluded that land area influences land prices.