These two sets of data should be unrelated, but let\'s see... Use your prefered

Question

These two sets of data should be unrelated, but let's see...

Use your prefered method (Excel, GeoGebra, graphing calculator...) to answer the following questions.

There are detailed instructions for using GeoGebra and Excel in the Section 4.3 notes on the class website.

Round all numbers to at least four decimal places.

Calculate the correlation coefficient.

r=

Calculate the equation of the line of best fit.

f(x)=

Consider the following table Revenue from arcades Number of Computer Science Year in the U.S., in billions PhDs awarded in the U.S. 2000 1.25 882 847 2001 1.23 1.42 900 2002 919 1.24 2003 937 2004 1.35 1.5 1104 2005 2006 1.67 1470 2007 1.71 1632 1.72 2008 1746 2009 1.88 1582

Explanation / Answer

X Values 1.25 1.23 1.42 1.24 1.35 1.5 1.67 1.71 1.72 1.88

Y Values 882 847 900 919 937 1104 1470 1632 1746 1582

X - Mx

-0.247
-0.267
-0.077
-0.257
-0.147
0.003
0.173
0.213
0.223
0.383

Mx: 1.497

Y - My

-319.900
-354.900
-301.900
-282.900
-264.900
-97.900
268.100
430.100
544.100
380.100

My: 1201.900

(X - Mx)2

0.061
0.071
0.006
0.066
0.022
0.000
0.030
0.045
0.050
0.147

Sum: 0.498

(Y - My)2

102336.010
125954.010
91143.610
80032.410
70172.010
9584.410
71877.610
184986.010
296044.810
144476.010

Sum: 1176606.900

(X - Mx)(Y - My)

79.015
94.758
23.246
72.705
38.940
-0.294
46.381
91.611
121.334
145.578

Sum: 713.277

Result Details & Calculation

X Values
= 14.97
Mean = 1.497
(X - Mx)2 = SSx = 0.498

Y Values
= 12019
Mean = 1201.9
(Y - My)2 = SSy = 1176606.9

X and Y Combined
N = 10
(X - Mx)(Y - My) = 713.277

R Calculation
r = ((X - My)(Y - Mx)) / ((SSx)(SSy))

r = 713.277 / ((0.498)(1176606.9)) = 0.9322

Meta Numerics (cross-check)

Key

X: X Values
Y: Y Values
Mx: Mean of X Values
My: Mean of Y Values
X - Mx & Y - My: Deviation scores
(X - Mx)2 & (Y - My)2: Deviation Squared
(X - Mx)(Y - My): Product of Deviation Scores

The value of R is 0.9322. This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).

The value of R2, the coefficient of determination, is 0.869.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.