Question

Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ thousands) last month for each client sampled.

Number of Contacts, X		Sales ($ thousands), Y		Number of Contacts, X		Sales ($ thousands), Y
14		24		23		30
12		14		48		90
20		28		50		85
16		30		55		120
46		80		50		110

  

(a)	Determine the standard error of estimate. (Round your answer to 2 decimal places.)

Standard error of estimate

Answer 1

The given data is

Use R to run a linear regression and find the standard error.

X <- c(14,12,20,16,46,23,48,50,55,50)
Y <- 1000*c(24,14,28,30,80,30,90,85,120,110)
fit <- lm(Y ~ X)
summary(fit)

The output is:

Call:

lm(formula = Y ~ X)

Residuals:

Min 1Q Median 3Q Max

-12531 -7130 -1638 6684 12469

Coefficients:

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

(Intercept) -12201.0 6559.6 -1.86 0.0999 .  

X 2194.6 175.5 12.51 1.56e-06 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9310 on 8 degrees of freedom

Multiple R-squared: 0.9513, Adjusted R-squared: 0.9452

F-statistic: 156.4 on 1 and 8 DF, p-value: 1.565e-06

The standard error of the estimate is calculated as

.

This is same as Residual standard error: 9,310

X = (14, 12, 20, 16, 46,23,48,50,55,50) Y = 1000(24, 14, 28, 30, 80, 30, 90, 85, 120, 110)