This table is to test the significance of the Regression model, which is >0.05 in our example (not significant) The last tableĬoefficients of Intercept means the Intercept, while Coefficients of Year of services mean the slope. R Square is known as Coefficient of Determination, it measures how many percentage of variation in Y can be explained by variation in X, it is 49% in our example. In our example, 0.7 shows a strong positive relation. +1 is a linear relation, 0 is no relation, -1 is negative linear relation. Multiple R is known as Multiple Coefficient of Correlation. Note that X Range is the independent variable while Y Range is the dependent variable. Navigate to DATA tab > Data Analysis > Regression > OK Y = 933.3333 + 2114.286X Simple Linear Regression – using Excel Data Analysisīefore we begin, make sure you have installed Analysis Toolpak Add-in Y-intercept = mean of y - slope * (mean of x)Īlternatively, we can calculate intercept using INTERCEPT Function =INTERCEPT(array y, array x)
To calculate the y-intercept, use formula mean of y = slope * (mean of x) + y-intercept
To calculate the slope, use formula slope b = covariance x y / variance of xĪlternatively, we can calculate slope using Slope Function =SLOPE(array y, array x) =SLOPE(B2:B7,A2:A7) =2114.286 Next, calculate sample variance of X using VAR.S Function =VAR.S(A1:A7) In this example, Year of services is an independent variable (X), while Salary is a dependent variable (Y).įirst of all, calculate the sample covariance x y using COVARIANCE.S Function =COVARIANCE.S(A2:A7, B2:B7) Simple Linear Regression – semi-auto calculationĪssume that we want to analyze the relationship between year of services and salary, we draw a sample of 6 employees as below. In order to find the equation, we use Least Squares Method to help us find a (intercept) and b (slope). The regression line equation of simple linear regression is represented as Y = a + bX (same as y=mx + c which we learned in elementary school) For multiple independent variables, we call it multiple linear regression. If the linear regression model only has one independent variable, we call it simple linear regression. The straight line is known as least squares or regression line. We draw a random sample from the population and draw the best fitting straight line in order to estimate the population. Regression analysis is to predict the value of one interval variable based on another interval variable(s) by a linear equation. SPSS Excel Multiple Regression Simple Linear Regression This SPSS Excel tutorial explains how to run Simple Linear Regression in SPSS and Excel.
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