linear_regression
Arvind Sharma
2024-04-23
# Clear the workspace
rm(list = ls()) # Clear environment
gc() # Clear unused memory## used (Mb) gc trigger (Mb) limit (Mb) max used (Mb)
## Ncells 531014 28.4 1182544 63.2 NA 669277 35.8
## Vcells 973384 7.5 8388608 64.0 16384 1840364 14.1 cat("\f") # Clear the console1 Data
1.1 Export Data to Excel
?attitude
df <- attitude
getwd()## [1] "/Users/arvindsharma/Library/CloudStorage/Dropbox/WCAS/Data Analysis/Data Analysis - Spring II 2024/Data Analysis - Spring II 2024 (shared files)/W6/Week 14"write.csv(x = df, file = "attitude_data")2 Simple Linear Regression
\[ rating_i = \beta_0 + \beta_1 \ complaints_i + \epsilon_i \]
model1 <- lm(formula = df$rating ~ df$complaints)
model1 <-
lm(data = df,
formula = rating ~ complaints)
summary(model1)##
## Call:
## lm(formula = rating ~ complaints, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.8799 -5.9905 0.1783 6.2978 9.6294
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 14.37632 6.61999 2.172 0.0385 *
## complaints 0.75461 0.09753 7.737 1.99e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.993 on 28 degrees of freedom
## Multiple R-squared: 0.6813, Adjusted R-squared: 0.6699
## F-statistic: 59.86 on 1 and 28 DF, p-value: 1.988e-082.1 Slope
?var
cov(x = df$complaints, y = df$rating)## [1] 133.7793var(x = df$complaints)## [1] 177.2828beta_1 <- cov(x = df$complaints, y = df$rating)/var(x = df$complaints)
beta_1## [1] 0.75460982.2 Intercept
beta_0 <-
mean(df$rating) - mean(df$complaints) * beta_1
beta_0## [1] 14.376323 Multivariate Linear Regression
model2 <-
lm(data = df,
formula = rating ~ .)
summary(model2)##
## Call:
## lm(formula = rating ~ ., data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.9418 -4.3555 0.3158 5.5425 11.5990
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.78708 11.58926 0.931 0.361634
## complaints 0.61319 0.16098 3.809 0.000903 ***
## privileges -0.07305 0.13572 -0.538 0.595594
## learning 0.32033 0.16852 1.901 0.069925 .
## raises 0.08173 0.22148 0.369 0.715480
## critical 0.03838 0.14700 0.261 0.796334
## advance -0.21706 0.17821 -1.218 0.235577
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.068 on 23 degrees of freedom
## Multiple R-squared: 0.7326, Adjusted R-squared: 0.6628
## F-statistic: 10.5 on 6 and 23 DF, p-value: 1.24e-05library(stargazer)##
## Please cite as:## Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2.3. https://CRAN.R-project.org/package=stargazerstargazer(model1, model2, type="text")##
## =================================================================
## Dependent variable:
## ---------------------------------------------
## rating
## (1) (2)
## -----------------------------------------------------------------
## complaints 0.755*** 0.613***
## (0.098) (0.161)
##
## privileges -0.073
## (0.136)
##
## learning 0.320*
## (0.169)
##
## raises 0.082
## (0.221)
##
## critical 0.038
## (0.147)
##
## advance -0.217
## (0.178)
##
## Constant 14.376** 10.787
## (6.620) (11.589)
##
## -----------------------------------------------------------------
## Observations 30 30
## R2 0.681 0.733
## Adjusted R2 0.670 0.663
## Residual Std. Error 6.993 (df = 28) 7.068 (df = 23)
## F Statistic 59.861*** (df = 1; 28) 10.502*** (df = 6; 23)
## =================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01library(readxl)
attitude <- read_excel("~/Library/CloudStorage/Dropbox/WCAS/Data Analysis/Data Analysis - Fall 2023/Data Analysis - Fall 2023 (shared files)/Week 15/attitude_2.xls",
sheet = "Sheet4", range = "A1:I31")
model3 <-
lm(data = attitude,
formula = rating ~ .)
summary(model3)##
## Call:
## lm(formula = rating ~ ., data = attitude)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.5940 -4.8315 0.3552 5.5677 10.9790
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.06433 12.02017 0.837 0.41144
## complaints 0.59792 0.17054 3.506 0.00199 **
## privileges -0.05822 0.14549 -0.400 0.69289
## learning 0.32029 0.17188 1.863 0.07580 .
## raises 0.09673 0.23039 0.420 0.67866
## critical 0.04266 0.15048 0.283 0.77945
## advance -0.23265 0.18776 -1.239 0.22838
## male 1.00077 3.02258 0.331 0.74370
## female NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.209 on 22 degrees of freedom
## Multiple R-squared: 0.7339, Adjusted R-squared: 0.6493
## F-statistic: 8.669 on 7 and 22 DF, p-value: 4.1e-05stargazer(model1, model2,model3, type="text")##
## =======================================================================================
## Dependent variable:
## -------------------------------------------------------------------
## rating
## (1) (2) (3)
## ---------------------------------------------------------------------------------------
## complaints 0.755*** 0.613*** 0.598***
## (0.098) (0.161) (0.171)
##
## privileges -0.073 -0.058
## (0.136) (0.145)
##
## learning 0.320* 0.320*
## (0.169) (0.172)
##
## raises 0.082 0.097
## (0.221) (0.230)
##
## critical 0.038 0.043
## (0.147) (0.150)
##
## advance -0.217 -0.233
## (0.178) (0.188)
##
## male 1.001
## (3.023)
##
## female
##
##
## Constant 14.376** 10.787 10.064
## (6.620) (11.589) (12.020)
##
## ---------------------------------------------------------------------------------------
## Observations 30 30 30
## R2 0.681 0.733 0.734
## Adjusted R2 0.670 0.663 0.649
## Residual Std. Error 6.993 (df = 28) 7.068 (df = 23) 7.209 (df = 22)
## F Statistic 59.861*** (df = 1; 28) 10.502*** (df = 6; 23) 8.669*** (df = 7; 22)
## =======================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01plot(model3)
