STAT 245 Lecture Notes - Lecture 10: Scatter Plot
STAT 245.3 – CORRELATION & REGRESSION
Exercises #10 - Solution
Ten students who graduated from university in 2000 with a degree in a Social Science were
interviewed in 2011 with the following information on incomes collected. That data is reported in
$1000’s. A scatterplot of the data is given, together with the least-squares regression line.
Graduate
A
B
C
D
E
F
G
H
I
J
Income in 2000 (X)
30
32
37
34
30
34
39
42
38
37
Income in 2011 (Y)
64
68
78
70
66
72
76
80
74
74
x = 2000
y=2011
52504846444240
92.5
90.0
87.5
85.0
82.5
80.0
77.5
75.0
Scatterplot of Incomes: 2011 vs 2000
SOME SUMMARY QUANTITIES
i
x 353
i
y 722
2
i
x 12,603
2
i
y 52,372
ii
x y 25,664
Document Summary
Ten students who graduated from university in 2000 with a degree in a social science were interviewed in 2011 with the following information on incomes collected. A scatterplot of the data is given, together with the least-squares regression line. Determine the sample correlation coefficient and comment upon its value. r n. 2 x i n x y i i x i y i. Determine the equation of the least-squares regression line. n b n x y i i. 2 x i x i a y bx. 90 915 of the variability in 2011 incomes. R is explained by their linear relationship with 2000 incomes. The predicted 2011 income for this graduate who earned ,000 in 2000 is ,557 (to the nearest dollar) 0 01 and conclude that is significantly greater than zero. The conclusion in question [5] is that the correlation is significantly greater than zero.
