Question

Use the appropriate test to determine if the effect of galleys for a manuscript (X) on the total dollar cost of correcting typographical errors (Y) in technical manuscripts can be justifiably represented by a regression-through-the-origin model. Find (i) value of the test statistic, (ii) critical value at 2% level of significance, and (iii) p-value of the test. The linear regression function does through the origin, the estimated regression function is Y-hat=18.0283X

show me the R code please.

Y X
128.0 7.0
213.0 12.0
191.0 10.0
178.0 10.0
250.0 14.0
446.0 25.0
540.0 30.0
457.0 25.0
324.0 18.0
177.0 10.0
75.0 4.0
107.0 6.0

Answer 1

i) Value of the test statistic =(Estimate/Standard error)=226.8

ii) critical value at 2% significance level=t(.01,11)=2.718079 (Here the critical region is |t|>t(.01,11))

iii) Two sided p value =2*P(t₁₁>226.8), which is almost zero (actually less than 2x10^(-16))

R Output

Residuals:
Min 1Q Median 3Q Max
-4.708 -2.618 -1.010 2.073 10.717

Coefficients:
Estimate Std. Error t value Pr(>|t|)
x 18.02830 0.07948 226.8 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.507 on 11 degrees of freedom
Multiple R-squared: 0.9998, Adjusted R-squared: 0.9998
F-statistic: 5.145e+04 on 1 and 11 DF, p-value: < 2.2e-16

R Code

y=c(128,213,191,178,250,446,540,457,324,177,75,107)
x=c(7,12,10,10,14,25,30,25,18,10,4,6)
w=lm(y~x-1)
summary(w)