Question

The data below was obtained in a study of number of hours spent by a salesman in a day (x) versus the number of cars sold (y) by the salesman.

x	y
1	1
2	1
3	2
4	3
5	5

a) The correlation coefficient r between X and Y is close to

b)The estimated coefficients of regression line (y = ?₀ + ?₁x) are:

c)If the number of hours spent is 3, what is the predicted sales

d)Consider the observed data: number of hours spent is 3, and number of cars sold is 2. What is the residual of this observation:

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -0.6 + 1 x
Sample size: 5
R (correlation coefficient) = 0.94491118
R-sq = 0.89285714
Estimate of error standard deviation: 0.63245553

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	-0.6	0.66332496	? 0	3	-0.90453403	0.4324
Slope	1	0.2	? 0	3	5	0.0154

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	10	10	25	0.0154
Error	3	1.2	0.4
Total	4	11.2

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	95% C.I. for mean	95% P.I. for new
3	2.4	0.28284271	(1.4998683, 3.3001317)	(0.19513652, 4.6048635)

Hence,

a) Correlation coefficient = 0.9449

b) Regression equation: y = -0.6 + x

c) For x = 3: y = 2.4

d) Residual = Actual value - Estimated value = 2 - 2.4 = -0.4