Quarto enables you to weave together content and executable code into a finished document. To learn more about Quarto see https://quarto.org.
When you click the Render button a document will be generated that includes both content and the output of embedded code. You can embed code like this:
1. Draw a scatter plot of Y vs X:
library(readr)
gpa <- read_csv("C:/Users/korra/Downloads/GPA.csv",col_names = TRUE)Rows: 120 Columns: 2
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
dbl (2): Y, X
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.#head(gpa)
# Scatterplot
plot(gpa$X, gpa$Y, xlab = "ACT Scores", ylab = "GPA", main = "Scatterplot of GPA vs ACT Scores")
2. Fit a regression model and write down the estimated regression function:
# Fit a linear regression model
model<-lm(Y~X,data=gpa)
# Print the estimated regression function
coefficients <- coef(model)
cat("Regression function: Y =", round(coefficients[2], 4), "* X +", round(coefficients[1], 4), "\n")Regression function: Y = 0.0388 * X + 2.114 \[ Y = 0.0388 * X + 2.114\]
3. Plot the estimated regression line and the data
model<-lm(Y~X,data=gpa)
summary(model)$coefficients Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.11404929 0.32089483 6.587982 1.304450e-09
X 0.03882713 0.01277302 3.039777 2.916604e-03# Scatterplot
plot(gpa$X, gpa$Y, xlab = "ACT Scores", ylab = "GPA", main = "Scatterplot of GPA vs ACT Scores")
points(gpa$X,model$fit, type="l", col="red")
4. Point estimate of the change in the mean response when the entrance test score increases by one point \[\beta_1 = 0.0388\] 5. Obtain a 99 percent confidence interval for β1
conf_int <- confint(model, level = 0.99)
cat("99% Confidence Interval for β1:", round(conf_int[2, ], 4), "\n")99% Confidence Interval for β1: 0.0054 0.0723 cat(" The confidence interval does", ifelse(0 >= conf_int[2, 1] & 0 <= conf_int[2, 2], "include", "not include"), "zero.\n") The confidence interval does not include zero.This means we are 99% confident that for an additional ACT Score, the GPA increases by between 0.0054 and 0.0723 points.
6. Test for linear association between student’s ACT score and GPA at a significance level of 0.05