getwd()[1] "/cloud/project"[1]“/cloud/project”
launch<-read.csv("challenger2.csv")View(launch)#Estimate beta mannually
b<-cov(launch$temperature,launch$distress_ct)/var(launch$temperature)
b[1] -0.03364796#estimate alpha manually
a<-mean(launch$distress_ct)-b*mean((launch$temperature))
a[1] 2.814585#Let us get the correlation between temperature and distress
r<-cor(launch$temperature,launch$distress_ct)#computing the slope using correlation
r*(sd(launch$distress_ct)/sd(launch$temperature))[1] -0.03364796model<-lm(distress_ct~temperature,data = launch)
model
Call:
lm(formula = distress_ct ~ temperature, data = launch)
Coefficients:
(Intercept) temperature
2.81458 -0.03365 summary(model)
Call:
lm(formula = distress_ct ~ temperature, data = launch)
Residuals:
Min 1Q Median 3Q Max
-1.0649 -0.4929 -0.2573 0.3052 1.7090
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.81458 1.24629 2.258 0.0322 *
temperature -0.03365 0.01815 -1.854 0.0747 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.7076 on 27 degrees of freedom
Multiple R-squared: 0.1129, Adjusted R-squared: 0.08004
F-statistic: 3.436 on 1 and 27 DF, p-value: 0.07474#creating a SL Function
reg <- function(y, x) {
# Ensure x is a matrix
x <- as.matrix(x)
# Add the intercept term to x
x <- cbind(1, x) # 1 is the intercept term
# Solve for the regression coefficients using the normal equation
b <- solve(t(x) %*% x) %*% t(x) %*% y
# Assign column name to the result
colnames(b) <- "estimate"
# Print the regression coefficients
print(b)
}str(launch)'data.frame': 29 obs. of 4 variables:
$ distress_ct : int 0 1 0 0 0 0 0 0 1 1 ...
$ temperature : int 66 70 69 68 67 72 73 70 57 63 ...
$ field_check_pressure: int 50 50 50 50 50 50 100 100 200 200 ...
$ flight_num : int 1 2 3 4 5 6 7 8 9 10 ...reg(y=launch$distress_ct,x=launch[2:4]) estimate
2.239817e+00
temperature -3.124185e-02
field_check_pressure -2.586765e-05
flight_num 2.762455e-02summary(model)
Call:
lm(formula = distress_ct ~ temperature, data = launch)
Residuals:
Min 1Q Median 3Q Max
-1.0649 -0.4929 -0.2573 0.3052 1.7090
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.81458 1.24629 2.258 0.0322 *
temperature -0.03365 0.01815 -1.854 0.0747 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.7076 on 27 degrees of freedom
Multiple R-squared: 0.1129, Adjusted R-squared: 0.08004
F-statistic: 3.436 on 1 and 27 DF, p-value: 0.07474model<-lm(distress_ct ~ temperature + field_check_pressure + flight_num, data = launch)
model
Call:
lm(formula = distress_ct ~ temperature + field_check_pressure +
flight_num, data = launch)
Coefficients:
(Intercept) temperature field_check_pressure
2.240e+00 -3.124e-02 -2.587e-05
flight_num
2.762e-02 #we obtained the same valuessummary (model)
Call:
lm(formula = distress_ct ~ temperature + field_check_pressure +
flight_num, data = launch)
Residuals:
Min 1Q Median 3Q Max
-1.2744 -0.3335 -0.1657 0.2975 1.5284
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.240e+00 1.267e+00 1.767 0.0894 .
temperature -3.124e-02 1.787e-02 -1.748 0.0927 .
field_check_pressure -2.587e-05 2.383e-03 -0.011 0.9914
flight_num 2.762e-02 1.798e-02 1.537 0.1369
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.6926 on 25 degrees of freedom
Multiple R-squared: 0.2132, Adjusted R-squared: 0.1188
F-statistic: 2.259 on 3 and 25 DF, p-value: 0.1063#there isn't enough evidence to reject the null with any of the coefficients, even they might affect.