2. Consider a set of data (i, yi), i = 1,..., 72, provided in Table 3. If we believe that ; and y; has a linear relationship, we may apply simple linear regression to fit these data to a linear model. More precisely, we try to find a and ẞ such that the straight line y = a + ẞx minimizes the sum of squared errors for all the data points: x 38 min a.3 |3 [yi - (a + ẞz;)]². y 137 56 201 50 152 52 107 37 150 60 173 67 194 54 166 59 154 43 137 30 38 53 193 59 40 65 Table 3: Data for Problem 2 154 175 247 While almost all statistical software and packages provide tools for one to solve the above linear regression problem, we may also consider it as a nonlinear program and solve it with an optimization solver (e.g., MS Excel solver). For the data provided in the following table, solve the linear regression problem. Write down the optimal ẞ you find by rounding it to the first digit after the decimal point (e.g., 9.011, 1.229, and 3.245 should be rounded to 9.01, 1.23, and 3.25 to be written down).
2. Consider a set of data (i, yi), i = 1,..., 72, provided in Table 3. If we believe that ; and y; has a linear relationship, we may apply simple linear regression to fit these data to a linear model. More precisely, we try to find a and ẞ such that the straight line y = a + ẞx minimizes the sum of squared errors for all the data points: x 38 min a.3 |3 [yi - (a + ẞz;)]². y 137 56 201 50 152 52 107 37 150 60 173 67 194 54 166 59 154 43 137 30 38 53 193 59 40 65 Table 3: Data for Problem 2 154 175 247 While almost all statistical software and packages provide tools for one to solve the above linear regression problem, we may also consider it as a nonlinear program and solve it with an optimization solver (e.g., MS Excel solver). For the data provided in the following table, solve the linear regression problem. Write down the optimal ẞ you find by rounding it to the first digit after the decimal point (e.g., 9.011, 1.229, and 3.245 should be rounded to 9.01, 1.23, and 3.25 to be written down).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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Question
Consider a set of data ...
![2. Consider a set of data (i, yi), i = 1,..., 72, provided in Table 3. If we believe that ; and y; has a linear
relationship, we may apply simple linear regression to fit these data to a linear model. More precisely, we try
to find a and ẞ such that the straight line y = a + ẞx minimizes the sum of squared errors for all the data
points:
x
38
min
a.3
|3
[yi - (a + ẞz;)]².
y
137
56
201
50
152
52
107
37
150
60
173
67
194
54
166
59
154
43
137
30
38
53
193
59
40
65
Table 3: Data for Problem 2
154
175
247
While almost all statistical software and packages provide tools for one to solve the above linear regression
problem, we may also consider it as a nonlinear program and solve it with an optimization solver (e.g., MS
Excel solver). For the data provided in the following table, solve the linear regression problem. Write down the
optimal ẞ you find by rounding it to the first digit after the decimal point (e.g., 9.011, 1.229, and 3.245 should
be rounded to 9.01, 1.23, and 3.25 to be written down).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14d1509a-ace2-4c34-80af-3d3ea4af9d72%2Fbd250233-dc6c-4059-9b39-8cd930bc7ffa%2Fg6r1phi_processed.png&w=3840&q=75)
Transcribed Image Text:2. Consider a set of data (i, yi), i = 1,..., 72, provided in Table 3. If we believe that ; and y; has a linear
relationship, we may apply simple linear regression to fit these data to a linear model. More precisely, we try
to find a and ẞ such that the straight line y = a + ẞx minimizes the sum of squared errors for all the data
points:
x
38
min
a.3
|3
[yi - (a + ẞz;)]².
y
137
56
201
50
152
52
107
37
150
60
173
67
194
54
166
59
154
43
137
30
38
53
193
59
40
65
Table 3: Data for Problem 2
154
175
247
While almost all statistical software and packages provide tools for one to solve the above linear regression
problem, we may also consider it as a nonlinear program and solve it with an optimization solver (e.g., MS
Excel solver). For the data provided in the following table, solve the linear regression problem. Write down the
optimal ẞ you find by rounding it to the first digit after the decimal point (e.g., 9.011, 1.229, and 3.245 should
be rounded to 9.01, 1.23, and 3.25 to be written down).
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