> setwd("~/Downloads")

> # read data from Excel/csv file
> mail <- read.table("mail(1).csv",header = TRUE,sep=",")

> # scatter diagram
>
> plot(mail$orders, mail$weight, col="red",xlab="order amount",ylab="weight",
+      xlim=range(mail$orders),ylim=range(mail$we .... [TRUNCATED]

> # using lm to fit linear model, use hardness to predict strength,
> # tensile strength should be dependent variable
> mod = lm(formula = weight ~ o .... [TRUNCATED]

> # using the summary() function to call output of the above model,
> # output includes coefficients of intercept, slope,residuals, R-squared etc.
> .... [TRUNCATED]

Call:
lm(formula = weight ~ orders, data = mail)

Residuals:
    Min      1Q  Median      3Q     Max
-48.252 -15.772  -2.157   9.047  58.056

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)    5.552     15.780   0.352    0.728
orders        32.760      1.137  28.824   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 24.1 on 23 degrees of freedom
Multiple R-squared:  0.9731,	Adjusted R-squared:  0.9719
F-statistic: 830.8 on 1 and 23 DF,  p-value: < 2.2e-16


> # using least squares method to determine b0 and b1
> sy <- sd(mail$orders)  # sample standard deviation of dependent variable Y

> sx <- sd(mail$weight)

> r <- cor(mail$orders,mail$weight) # correlation coefficient between X and Y

> avgX <- mean(mail$weight)

> avgY <- mean(mail$orders)

> # you should obtain the same results given by function "lm" above
> b1 <- r*sy/sx

> b0 <- avgY-b1*avgX

> # retrieve coefficient of determination r-squared
> summary(mod)$r.squared
[1] 0.9730622

> b0 + b1*500
[1] 15.04256

> #R squared
> summary(mod)$r.square
[1] 0.9730622

> sse <- sum((fitted(mod) - mean(mail$weight))^2)

> ssr <- sum((fitted(mod) - mail$weight)^2)

> 1 - (ssr/(sse + ssr))
[1] 0.9730622