Given the following data set with x the amount of product ma

Given the following data set with x the amount of product manufactured in one month in millions of pounds as and y as the payroll for one month in hundred thousand dollars

X: 1.61, 3.17, 3.65, 4.26, 3.38, 6.19, 7.39, 8.66, 9.37, 9.44, 11.3, 11.18, 12.03, 13.14, 15.9, 15.67

And Y: 3.77, 13.48, 12, 15.54, 13.81, 18.93, 25.88, 28.1, 28.08, 31.16, 37.01, 30.75, 39.4, 42.54, 51.55, 48.91

Estimate with 70% confidence, the average change in monthly payroll when monthly production increases by 1 million pounds. Show all relevant work and be careful to convert units correctly

Solution

Let assume that the regression equation is

Y=b₀+b₁X

Using R-language

x=c(1.61, 3.17, 3.65, 4.26, 3.38, 6.19, 7.39, 8.66, 9.37, 9.44, 11.3, 11.18, 12.03, 13.14, 15.9, 15.67)
y=c(3.77, 13.48, 12, 15.54, 13.81, 18.93, 25.88, 28.1, 28.08, 31.16, 37.01, 30.75, 39.4, 42.54, 51.55, 48.91)
z=lm(y~x)
summary(z)

> summary(z)

Call:
lm(formula = y ~ x)

Residuals:
Min 1Q Median 3Q Max
-4.9340 -0.8753 0.8298 1.1979 2.2805

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.5097 1.1088 1.362 0.195
x 3.0567 0.1157 26.414 2.41e-13 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.028 on 14 degrees of freedom
Multiple R-squared: 0.9803, Adjusted R-squared: 0.9789
F-statistic: 697.7 on 1 and 14 DF, p-value: 2.408e-13