Question

x=c(	13,	18,	36,	43,	45,	116)
y=c(	270,	350,	470,	500,	560,	1280)

# Construct a scatterplot using R.
plot(x,y)

# Calculate the least squares regression line
mod = lm(y~x)
summary(mod)

# Correlation
cor(x,y)

(b) From the R output give the equation of the estimated regression line. (Round all numerical values to two decimal places.)

(c) What is the correlation coefficient r? (Round your answer to three decimal places.)

(d) Because the largest x value in the sample greatly exceeds the others, this observation may have been very influential in determining the equation of the line. Delete this observation and recalculate the equation. (Round all numerical values to two decimal places.)

Answer 1

>x=c(13,18,36,43,45,116)
>y=c(270,350,470,500,560,1280)

# Construct a scatter plot using R.
>plot(x,y)

(b) Calculate the least squares regression line
>mod = lm(y~x)

8 8 120 100

>mod

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x
131.82 9.74

> summary(mod)

Call:
lm(formula = y ~ x)

Residuals:
1 2 3 4 5
-17.7622 22.7273 0.4895 -24.8252 19.3706

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 185.0350 28.3283 6.532 0.00729 **
x 7.9021 0.8417 9.388 0.00256 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 24.66 on 3 degrees of freedom
Multiple R-squared: 0.9671,   Adjusted R-squared: 0.9561
F-statistic: 88.13 on 1 and 3 DF, p-value: 0.002561

(c) Correlation

>cor(x,y)

[1] 0.996

(d) After removing largest x value

> x=c(13,18,36,43,45)
> y=c(270,350,470,500,560)
> mod=lm(y~x)
> mod

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x
185.04     7.90