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(t_{11}>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)*

home / study / math / statistics and probability / statistics
and probability questions and answers / use the appropriate test to
determine if the effect of galleys for a manuscript (x) on the
...
Question: Use the appropriate test to determine if the
effect of galleys for a manuscript (X) on the total ...
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)...

Q.4.12. Typographical errors. Shown below are the number of
galleys for a manuscript (X) and the total dollar cost of
correcting typographical errors (Y) i a random sample of recent
orders handled by a firm specializing in technical manuscripts.
Since Y involves variable costs only, an analyst wished to
determine whether regression-through-the-origin model (4.10) is
appropriate for studying the relation between the two
variables.
i: 1 2 3 4 5 6 7 8 9 10 11 12
Xi: 7 12...

We wish to determine the impact of Specification Buying, X11, on
Satisfaction Level, X10. To do so we will split the Hatco data file
into two separate data sets based on the Specification Buying, X11.
This variable has two categories:
1=employs total value analysis approach, evaluating each
purchase separately;
0 = use of specification buying.
Sort the entire Hatco data set based on Specification Buying.
This will create two separate groups of records. Those records with
X11 = 0 and...

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