3 Data Radio ads Revenue 4 Jan 21 $8,350.0 5 Feb 6 Mar 7 Apr 8 May 9 Jun 10 Jul 11 Aug 180 $22,755.0 50 $13,455.0 195 $21,100.0 96 $15,000.0 44 $12,500.0 171 $20,700.0 135 $19,722.0 120 $16,115.0 12 Sep 13 Oct 75 $13,100.0 14 Nov 106 $15,670.0 15 Dec 198 $25,300.0 a) Plot on a 2-dimensional graph the above data with "Radio ads" on x-axis, "Revenue" on y-axis. Assuming there is a linear relation between "Revenue" and “Radio ads". Make a guess of the line of best fit L, in the form of y=kxtb for the above 12 points. Draw the guessed best-fit line on the coordinate system as well. e b) Manually calculate the Bo and B1 for the linear regression model using the formula given above. Draw the line of best fit Le based on the calculated Bo and B1. e c) The least-squares error is defined as below:e where ŷ; is the predicted value (through the best fit line) for a given x;, and E;= (y; – ŷ). Compute the least-squares errors for both L; and Le. Compare which line has a smaller least-squares error.
3 Data Radio ads Revenue 4 Jan 21 $8,350.0 5 Feb 6 Mar 7 Apr 8 May 9 Jun 10 Jul 11 Aug 180 $22,755.0 50 $13,455.0 195 $21,100.0 96 $15,000.0 44 $12,500.0 171 $20,700.0 135 $19,722.0 120 $16,115.0 12 Sep 13 Oct 75 $13,100.0 14 Nov 106 $15,670.0 15 Dec 198 $25,300.0 a) Plot on a 2-dimensional graph the above data with "Radio ads" on x-axis, "Revenue" on y-axis. Assuming there is a linear relation between "Revenue" and “Radio ads". Make a guess of the line of best fit L, in the form of y=kxtb for the above 12 points. Draw the guessed best-fit line on the coordinate system as well. e b) Manually calculate the Bo and B1 for the linear regression model using the formula given above. Draw the line of best fit Le based on the calculated Bo and B1. e c) The least-squares error is defined as below:e where ŷ; is the predicted value (through the best fit line) for a given x;, and E;= (y; – ŷ). Compute the least-squares errors for both L; and Le. Compare which line has a smaller least-squares error.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 2– simple linear regressione
The following is the simple linear regression model:
y = Bo+ Bixe
For a given set of (xi, Xi), i= 1 k, the following best-fit equation can be used to calculate the Bo
and Bi values,
B1
E, (xF) - (k+ *)
Bo = ỹ - Bıre
where (xi, yi) are observed values, ī is the mean= (E, x;), ỹ is the mean =
and the corresponding line is called the line of best fit.
Transcribed Image Text:3 Data
Radio ads
Revenue
4 Jan
21
$8,350.0
5 Feb
6 Mar
7 Apr
8 May
9 Jun
10 Jul
11 Aug
180
$22,755.0
50
$13,455.0
195
$21,100.0
96
$15,000.0
44
$12,500.0
171
$20,700.0
135
$19,722.0
12 Sep
13 Oct
120
$16,115.0
$13,100.0
$15,670.0
75
14 Nov
106
15 Dec
198
$25,300.0
a) Plot on a 2-dimensional graph the above data with "Radio ads" on x-axis, "Revenue" on
y-axis.e
Assuming there is a linear relation between "Revenue" and "Radio ads". Make a guess of
the line of best fit Lg in the form of y=kxtb for the above 12 points. Draw the guessed
best-fit line on the coordinate system as well.
b) Manually calculate the Bo and Bi for the linear regression model using the formula given
above. Draw the line of best fit Le based on the calculated Bo and B1. e
c) The least-squares error is defined as below:e
where ŷ; is the predicted value (through the best fit line) for a given x;, and E;= (y; -
ŷi). Compute the least-squares errors for both Lg and Le. Compare which line has a
smaller least-squares error.
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