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<code>
rm(list = ls())

dat <- read.csv("http://commres.net/wiki/_media/regression01-bankaccount.csv")
head(dat)
attach(dat)

mod <- lm(bankaccount ~ income, data = dat)
summary(mod)
df.tot <- length(bankaccount) - 1
ss.tot <- var(bankaccount)*df.tot
var.tot <- var(bankaccount)

df.x <- length(income)-1
ss.x <- var(income)*df.x


m.y <- mean(bankaccount)
m.x <- mean(income)

sp.xy <- sum((income-m.x)*(bankaccount-m.y))
cov.xy <- sp.xy / df.tot
cov.xy 
cov(income, bankaccount)

sd.x <- sd(income)
sd.y <- sd(bankaccount)

r.xy <- cov.xy / (sd.x * sd.y)
r.xy
cor(income, bankaccount)

b <- sp.xy / ss.x
b
a <- m.y - (b * m.x)
a

y.pred <- a + (b * income)
y.pred
# mod$fitted.values
y.obs <- bankaccount
y.mean <- m.y

ss.xy <- sum((bankaccount-y.mean)^2)
ss.xy
ss.tot

ss.res <- sum((bankaccount-y.pred)^2)
ss.res

ss.reg <- sum((y.pred-y.mean)^2)
ss.reg

ss.reg + ss.res
ss.xy

df.tot
df.res <- length(bankaccount) - 1 - 1
df.reg <- 2 - 1

r.sq <- ss.reg / ss.xy
r.sq

sqrt(r.sq)
r.xy
cor(income, bankaccount)

se.b <- sqrt((ss.res/df.res)/ss.x)
se.b 
t.b <- b / se.b
t.b
p.b <- pt(t.b, df.res, lower.tail = F) * 2
p.b

ms.reg <- ss.reg / df.reg
ms.res <- ss.res / df.res
f.cal <- ms.reg / ms.res
f.cal
t.b^2
p.f <- pf(f.cal, df.reg, df.res, lower.tail = F)
p.f

summary(mod)
anova(mod)

a
b
se.b
t.b
p.b

r.sq
f.cal
p.f

</code>


<code>
> rm(list = ls())
> 
> dat <- read.csv("http://commres.net/wiki/_media/regression01-bankaccount.csv")
> head(dat)
  bankaccount income famnum
1           6    220      5
2           5    190      6
3           7    260      3
4           7    200      4
5           8    330      2
6          10    490      4
> attach(dat)
The following objects are masked from dat (pos = 4):

    bankaccount, famnum, income

The following objects are masked from dat (pos = 7):

    bankaccount, famnum, income

The following objects are masked from dat (pos = 8):

    bankaccount, famnum, income

The following objects are masked from dat (pos = 9):

    bankaccount, famnum, income

The following object is masked from df (pos = 10):

    income

The following object is masked from df (pos = 11):

    income

The following object is masked from df (pos = 12):

    income

The following object is masked from df (pos = 13):

    income

The following object is masked from df (pos = 15):

    income

> 
> mod <- lm(bankaccount ~ income, data = dat)
> summary(mod)

Call:
lm(formula = bankaccount ~ income, data = dat)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.5189 -0.8969 -0.1297  1.0058  1.5800 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept) 3.617781   1.241518   2.914  0.01947 * 
income      0.015269   0.004127   3.700  0.00605 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.176 on 8 degrees of freedom
Multiple R-squared:  0.6311,	Adjusted R-squared:  0.585 
F-statistic: 13.69 on 1 and 8 DF,  p-value: 0.006046

> df.tot <- length(bankaccount) - 1
> ss.tot <- var(bankaccount)*df.tot
> var.tot <- var(bankaccount)
> 
> df.x <- length(income)-1
> ss.x <- var(income)*df.x
> 
> 
> m.y <- mean(bankaccount)
> m.x <- mean(income)
> 
> sp.xy <- sum((income-m.x)*(bankaccount-m.y))
> cov.xy <- sp.xy / df.tot
> cov.xy 
[1] 137.7778
> cov(income, bankaccount)
[1] 137.7778
> 
> sd.x <- sd(income)
> sd.y <- sd(bankaccount)
> 
> r.xy <- cov.xy / (sd.x * sd.y)
> r.xy
[1] 0.7944312
> cor(income, bankaccount)
[1] 0.7944312
> 
> b <- sp.xy / ss.x
> b
[1] 0.01526906
> a <- m.y - (b * m.x)
> a
[1] 3.617781
> 
> y.pred <- a + (b * income)
> y.pred
 [1]  6.976973  6.518902  7.587736  6.671592  8.656569 11.099618  6.824283  9.420022
 [9]  8.503879  7.740426
> # mod$fitted.values
> y.obs <- bankaccount
> y.mean <- m.y
> 
> ss.xy <- sum((bankaccount-y.mean)^2)
> ss.xy
[1] 30
> ss.tot
[1] 30
> 
> ss.res <- sum((bankaccount-y.pred)^2)
> ss.res
[1] 11.06637
> 
> ss.reg <- sum((y.pred-y.mean)^2)
> ss.reg
[1] 18.93363
> 
> ss.reg + ss.res
[1] 30
> ss.xy
[1] 30
> 
> df.tot
[1] 9
> df.res <- length(bankaccount) - 1 - 1
> df.reg <- 2 - 1
> 
> r.sq <- ss.reg / ss.xy
> r.sq
[1] 0.631121
> 
> sqrt(r.sq)
[1] 0.7944312
> r.xy
[1] 0.7944312
> cor(income, bankaccount)
[1] 0.7944312
> 
> se.b <- sqrt((ss.res/df.res)/ss.x)
> se.b 
[1] 0.004127175
> t.b <- b / se.b
> t.b
[1] 3.699639
> p.b <- pt(t.b, df.res, lower.tail = F) * 2
> p.b
[1] 0.006045749
> 
> ms.reg <- ss.reg / df.reg
> ms.res <- ss.res / df.res
> f.cal <- ms.reg / ms.res
> f.cal
[1] 13.68733
> t.b^2
[1] 13.68733
> p.f <- pf(f.cal, df.reg, df.res, lower.tail = F)
> p.f
[1] 0.006045749
> 
> summary(mod)

Call:
lm(formula = bankaccount ~ income, data = dat)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.5189 -0.8969 -0.1297  1.0058  1.5800 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept) 3.617781   1.241518   2.914  0.01947 * 
income      0.015269   0.004127   3.700  0.00605 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.176 on 8 degrees of freedom
Multiple R-squared:  0.6311,	Adjusted R-squared:  0.585 
F-statistic: 13.69 on 1 and 8 DF,  p-value: 0.006046

> anova(mod)
Analysis of Variance Table

Response: bankaccount
          Df Sum Sq Mean Sq F value   Pr(>F)   
income     1 18.934 18.9336  13.687 0.006046 **
Residuals  8 11.066  1.3833                    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> 
> a
[1] 3.617781
> b
[1] 0.01526906
> se.b
[1] 0.004127175
> t.b
[1] 3.699639
> p.b
[1] 0.006045749
> 
> r.sq
[1] 0.631121
> f.cal
[1] 13.68733
> p.f
[1] 0.006045749
> 
> 
</code>