statistics r programing

Question

·        Generate random samples from Normal distribution with n=25 using RStudio for y

·        Generate random samples from Normal distribution with n=25 using RStudio for x1

·        Generate random samples from Normal distribution with n=25 using RStudio for x2

Solve the quations 1-4 using the generated data sets.

1.      Compute descriptive statistics (mean, mode, median, standart deviation, standart error of mean) for y, x1 and x2

2.      Obtain appropriate graphical presentation y, x1 and x2

3.      Investigate whether there is difference between population means of x1 and x2 at 0.05 significiance level.

4.      Investigate whether there is linear relationship between y and x1, x2.

Answer 1

Bunch of assumptions here which are probably wrong, concerning the random data. I picked values that are similar but not identical.

# generate 3 sets of random samples, mean and variance not specified

y <- rnorm(25,0,4)

x1 <- rnorm(25, 5, 4)

x2 <- rnorm(25, 3, 2)

library(psych)

describe(y, skew = FALSE, ranges = FALSE)

## vars n mean sd se

## X1 1 25 -0.41 3.73 0.75

median(y)

## [1] -0.126664

describe(x1, skew = FALSE, ranges = FALSE)

## vars n mean sd se

## X1 1 25 4.42 3.97 0.79

median(x1)

## [1] 4.515655

describe(x2, skew = FALSE, ranges = FALSE)

## vars n mean sd se

## X1 1 25 3.32 2.44 0.49

median(x2)

## [1] 3.593052

hist(y, xlim = c(-10,15), breaks = 13)

hist(x1, xlim = c(-10,15), breaks = 13)

hist(x2, xlim = c(-10,15), breaks = 13)

# two tailed t test (note: Ho is not rejected)

t.test(x1,x2)

##

## Welch Two Sample t-test

##

## data: x1 and x2

## t = 1.1762, df = 39.847, p-value = 0.2465

## alternative hypothesis: true difference in means is not equal to 0

## 95 percent confidence interval:

## -0.7877209 2.9804471

## sample estimates:

## mean of x mean of y

## 4.417515 3.321152

# regression analysis (note: Ho is not rejected for X1 or X2)

model.reg<-lm(y~x1+x2)

summary(model.reg)

##

## Call:

## lm(formula = y ~ x1 + x2)

##

## Residuals:

## Min 1Q Median 3Q Max

## -4.8797 -3.4752 -0.4957 2.5002 7.3344

##

## Coefficients:

## Estimate Std. Error t value Pr(>|t|)

## (Intercept) -1.7530 1.4316 -1.225 0.2337

## x1 0.3934 0.1819 2.163 0.0417 *

## x2 -0.1187 0.2962 -0.401 0.6924

## ---

## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##

## Residual standard error: 3.536 on 22 degrees of freedom

## Multiple R-squared: 0.1784, Adjusted R-squared: 0.1037

## F-statistic: 2.389 on 2 and 22 DF, p-value: 0.1151

plot(y,x1, ylab = "y", xlab = " ")

abline(a=coefficients(model.reg)[1], b=coefficients(model.reg)[2], col="red")

abline(a=coefficients(model.reg)[1], b=coefficients(model.reg)[3], col="blue")

legend("topright", legend=c("x1", "x2"),

col=c("red", "blue"), lty=1:1)