Below is some hypothetical data that shows the Rating (an index of how many peop
ID: 3338581 • Letter: B
Question
Below is some hypothetical data that shows the Rating (an index of how many people watch the show) and Average Cost for a 30-second advertisement for a number of game shows:
GAME SHOW
Rating
Is That Real Hair?
18.2
$55,000
Feng Shui Happy Booth
8.4
$20,000
Love Signals!
13.6
$26,000
How Many Worms?
11.9
$39,000
Spin the Bottle
9.0
$11,000
Wake that Possum!
22.6
$75,000
Sit on a Potato
3.5
$10,000
Name that Fruit!
2.1
$5,000
The $2.00 Question
4.6
$19,000
Conduct a full (five step) regressional analysis to answer this question:
Within the sample data, is an increase in ratings associated with an increase the average cost for a 30-second ad? If so, how much?
GAME SHOW
Rating
Average Cost for a 30 Second Ad ($)Is That Real Hair?
18.2
$55,000
Feng Shui Happy Booth
8.4
$20,000
Love Signals!
13.6
$26,000
How Many Worms?
11.9
$39,000
Spin the Bottle
9.0
$11,000
Wake that Possum!
22.6
$75,000
Sit on a Potato
3.5
$10,000
Name that Fruit!
2.1
$5,000
The $2.00 Question
4.6
$19,000
Explanation / Answer
r (correlation)=n(Exy)-(Ex)(Ey)/(nEx2-(Ex)2)(nEy2-(Ey)2)
=9(3913600)-(94)(260000)/ (9*11854000000-(260000)^2)(9*1358-(94)^2)
=0.937
r^2=0.88
Hence, we can say that when Average Cost for a 30 Second Ad ($) goes up, rating also goes up. Also, 88% of the variation in rating is accounted for by the Average Cost for a 30 Second Ad ($).
Rating (y) Avg Cost (x) x^2 y^2 xy 18.2 55000 3025000000 331.24 1001000 8.4 20000 400000000 70.56 168000 13.6 26000 676000000 184.96 353600 11.9 39000 1521000000 141.61 464100 9 11000 121000000 81 99000 22.6 75000 5625000000 510.76 1695000 3.5 10000 100000000 12.25 35000 2.1 5000 25000000 4.41 10500 4.6 19000 361000000 21.16 87400 94 260000 11854000000 1358 3913600Related Questions
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