7. Multiple Regression

7. Multiple Regression

• When there’s more than one predictor variable, simple linear regression becomes multiple linear regression
• The significance level is 0.05 if the corresponding confidence level is 95%. Therefore, p-value that is above 0.05 is not statistically significant and vice versa

7.1. Multiple Regression in Excel

• Data -> Data Analysis -> Regression
• If x = 85, y is 78.12
  • y = ax + bx + cx + d = 0.852(85) + -0.194(56) + 0.188(45) + 6.200 = 76.24
• Referring to the diagram below for summary output of excel:

7.2 Multiple Regression in R-Programming

• a <- c(77,50,71,72,81,94,96,99,67)
• b <- c(55,66,34,78,57,77,84,67,82)
• c <- c(66,63,72,77,56,54,66,75,88)
• y <- c(82,66,78,34,47,85,99,99,68)
• fit <- lm(y~a+b+c)

• y = 0.8520(a) + -0.1936(b) + 0.1880(c) + 6.2001
• Therefore when a is 85, b is 56, and c is 45, y = 76.24
  • y = 0.8520(85) + -0.1936(56) + 0.1880(45) + 6.2001 = 76.2385 = 76.24

Other useful functions of R-programming

• coefficients(fit) # model coefficients
• confint(fit, level=0.95) # CIs for model parameters
• fitted(fit) # predicted values
• residuals(fit) # residuals
• anova(fit) # anova table
• vcov(fit) # covariance matrix for model parameters