CW 3/25/25
Kayla Williams
2025-03-25
#library(readxl)
#Uploading the data
#ageandheight <- read_excel("AgeHeight.xl",sheet = "Hoja2")
#Creating the linear regression
#lmHeights = lm(height~age, data = AgeHeight)
#Review the results
#summary(lmHeights)
library(readxl)## Warning: package 'readxl' was built under R version 4.4.2AgeHeight <- read_excel("C:/Users/kayla/OneDrive/Documents/TSU/Adv_Topics_CS497/Classwork/AgeHeight.xlsx")
View(AgeHeight)
lm(formula = height~age,data = AgeHeight)##
## Call:
## lm(formula = height ~ age, data = AgeHeight)
##
## Coefficients:
## (Intercept) age
## 64.928 0.635R Markdown
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lmHeight = lm(height~age, data = AgeHeight)
lmHeight2 = lm(height~age + no_siblings, data = AgeHeight)
summary(lmHeight)##
## Call:
## lm(formula = height ~ age, data = AgeHeight)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.27238 -0.24248 -0.02762 0.16014 0.47238
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 64.9283 0.5084 127.71 < 2e-16 ***
## age 0.6350 0.0214 29.66 4.43e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.256 on 10 degrees of freedom
## Multiple R-squared: 0.9888, Adjusted R-squared: 0.9876
## F-statistic: 880 on 1 and 10 DF, p-value: 4.428e-11summary(lmHeight2)##
## Call:
## lm(formula = height ~ age + no_siblings, data = AgeHeight)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.26297 -0.22462 -0.02021 0.16102 0.49752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 64.90554 0.53526 121.260 8.96e-16 ***
## age 0.63751 0.02340 27.249 5.85e-10 ***
## no_siblings -0.01772 0.04735 -0.374 0.717
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2677 on 9 degrees of freedom
## Multiple R-squared: 0.9889, Adjusted R-squared: 0.9865
## F-statistic: 402.2 on 2 and 9 DF, p-value: 1.576e-09Including Plots
You can also embed plots, for example:
library(readr)## Warning: package 'readr' was built under R version 4.4.2library(psych)## Warning: package 'psych' was built under R version 4.4.3library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.4.3##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alphainsurance <- read_csv("C:/Users/kayla/OneDrive/Documents/TSU/Adv_Topics_CS497/Classwork/insurance.csv")## Rows: 1338 Columns: 7
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (3): sex, smoker, region
## dbl (4): age, bmi, children, expenses
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.View(insurance)
head(insurance)## # A tibble: 6 × 7
## age sex bmi children smoker region expenses
## <dbl> <chr> <dbl> <dbl> <chr> <chr> <dbl>
## 1 19 female 27.9 0 yes southwest 16885.
## 2 18 male 33.8 1 no southeast 1726.
## 3 28 male 33 3 no southeast 4449.
## 4 33 male 22.7 0 no northwest 21984.
## 5 32 male 28.9 0 no northwest 3867.
## 6 31 female 25.7 0 no southeast 3757.str(insurance)## spc_tbl_ [1,338 × 7] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ age : num [1:1338] 19 18 28 33 32 31 46 37 37 60 ...
## $ sex : chr [1:1338] "female" "male" "male" "male" ...
## $ bmi : num [1:1338] 27.9 33.8 33 22.7 28.9 25.7 33.4 27.7 29.8 25.8 ...
## $ children: num [1:1338] 0 1 3 0 0 0 1 3 2 0 ...
## $ smoker : chr [1:1338] "yes" "no" "no" "no" ...
## $ region : chr [1:1338] "southwest" "southeast" "southeast" "northwest" ...
## $ expenses: num [1:1338] 16885 1726 4449 21984 3867 ...
## - attr(*, "spec")=
## .. cols(
## .. age = col_double(),
## .. sex = col_character(),
## .. bmi = col_double(),
## .. children = col_double(),
## .. smoker = col_character(),
## .. region = col_character(),
## .. expenses = col_double()
## .. )
## - attr(*, "problems")=<externalptr>numeric_vars <- insurance[, sapply(insurance, is.numeric)]
cor(numeric_vars)## age bmi children expenses
## age 1.0000000 0.10934101 0.04246900 0.29900819
## bmi 0.1093410 1.00000000 0.01264471 0.19857626
## children 0.0424690 0.01264471 1.00000000 0.06799823
## expenses 0.2990082 0.19857626 0.06799823 1.00000000colnames(insurance)## [1] "age" "sex" "bmi" "children" "smoker" "region" "expenses"pairs(insurance[c("age", "bmi", "children", "expenses")])
model1 <- lm(expenses ~ age, data = insurance)
summary(model1)##
## Call:
## lm(formula = expenses ~ age, data = insurance)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8059 -6671 -5939 5440 47829
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3165.9 937.1 3.378 0.000751 ***
## age 257.7 22.5 11.453 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11560 on 1336 degrees of freedom
## Multiple R-squared: 0.08941, Adjusted R-squared: 0.08872
## F-statistic: 131.2 on 1 and 1336 DF, p-value: < 2.2e-16model2 <- lm(expenses ~ ., data = insurance)
summary(model2)##
## Call:
## lm(formula = expenses ~ ., data = insurance)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11302.7 -2850.9 -979.6 1383.9 29981.7
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11941.6 987.8 -12.089 < 2e-16 ***
## age 256.8 11.9 21.586 < 2e-16 ***
## sexmale -131.3 332.9 -0.395 0.693255
## bmi 339.3 28.6 11.864 < 2e-16 ***
## children 475.7 137.8 3.452 0.000574 ***
## smokeryes 23847.5 413.1 57.723 < 2e-16 ***
## regionnorthwest -352.8 476.3 -0.741 0.458976
## regionsoutheast -1035.6 478.7 -2.163 0.030685 *
## regionsouthwest -959.3 477.9 -2.007 0.044921 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6062 on 1329 degrees of freedom
## Multiple R-squared: 0.7509, Adjusted R-squared: 0.7494
## F-statistic: 500.9 on 8 and 1329 DF, p-value: < 2.2e-16plot(model2$residuals, main = "Residuals Plot", ylab = "Residuals", col = "#D02090")
insurance$age2 <- insurance$age^2
insurance$bmi30 <- ifelse(insurance$bmi >= 30, 1, 0)
model3 <- lm(expenses ~ age + age2 + children + bmi + sex + bmi30 * smoker + region, data = insurance)
summary(model3)##
## Call:
## lm(formula = expenses ~ age + age2 + children + bmi + sex + bmi30 *
## smoker + region, data = insurance)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17297.1 -1656.0 -1262.7 -727.8 24161.6
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 139.0053 1363.1359 0.102 0.918792
## age -32.6181 59.8250 -0.545 0.585690
## age2 3.7307 0.7463 4.999 6.54e-07 ***
## children 678.6017 105.8855 6.409 2.03e-10 ***
## bmi 119.7715 34.2796 3.494 0.000492 ***
## sexmale -496.7690 244.3713 -2.033 0.042267 *
## bmi30 -997.9355 422.9607 -2.359 0.018449 *
## smokeryes 13404.5952 439.9591 30.468 < 2e-16 ***
## regionnorthwest -279.1661 349.2826 -0.799 0.424285
## regionsoutheast -828.0345 351.6484 -2.355 0.018682 *
## regionsouthwest -1222.1619 350.5314 -3.487 0.000505 ***
## bmi30:smokeryes 19810.1534 604.6769 32.762 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4445 on 1326 degrees of freedom
## Multiple R-squared: 0.8664, Adjusted R-squared: 0.8653
## F-statistic: 781.7 on 11 and 1326 DF, p-value: < 2.2e-16Note that the echo = FALSE parameter was added to the
code chunk to prevent printing of the R code that generated the
plot.