1.2. Question 1 (q.2.1, page 75) - Theory Consider the following table based on a data set that has the sample size of 5 observations. - Ꮖ Image y Image 2 Image xy Image x- T Image (x)2 Image y - ỹ Image (x − ˜) (y — ÿ) ► Image - - 0 6 0 -2 (-2)² = 4 3.6 3.62-7.2 1 2 1 2 -1 (−1)² = 1 -0.4 -1 -0.4 0.4 2 3 4 6 0 0² = 0 0.6 3 1 9 3 1 (1)² = 1 -1.4 4 0 16 0 2 (2)² = 4 -2.4 0.0.60 1.-1.4-1.4 22.44.8 Στι ΣYi Σα ΣYixi Σ(xi) Image Σ(α; - π)2 Σ(y: - 3) - Σ(xi — x) (Yi — ÿ) 10 12 30 11 10 0 -13 (a) Using the values above, calculate the estimates for the intercept 61 and slope 62. (b) Using the numerical values above, show that Σ(x − x)² = - x² – Nò and Σ(xi - x) (yi – y) = Σ x iyi - Nx + y XiYi
1.2. Question 1 (q.2.1, page 75) - Theory Consider the following table based on a data set that has the sample size of 5 observations. - Ꮖ Image y Image 2 Image xy Image x- T Image (x)2 Image y - ỹ Image (x − ˜) (y — ÿ) ► Image - - 0 6 0 -2 (-2)² = 4 3.6 3.62-7.2 1 2 1 2 -1 (−1)² = 1 -0.4 -1 -0.4 0.4 2 3 4 6 0 0² = 0 0.6 3 1 9 3 1 (1)² = 1 -1.4 4 0 16 0 2 (2)² = 4 -2.4 0.0.60 1.-1.4-1.4 22.44.8 Στι ΣYi Σα ΣYixi Σ(xi) Image Σ(α; - π)2 Σ(y: - 3) - Σ(xi — x) (Yi — ÿ) 10 12 30 11 10 0 -13 (a) Using the values above, calculate the estimates for the intercept 61 and slope 62. (b) Using the numerical values above, show that Σ(x − x)² = - x² – Nò and Σ(xi - x) (yi – y) = Σ x iyi - Nx + y XiYi
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1.2. Question 1 (q.2.1, page 75) - Theory
Consider the following table based on a data set that has the sample size of 5 observations.
-
Ꮖ
Image y Image 2 Image xy
Image
x- T
Image
(x)2 Image y - ỹ Image (x − ˜) (y — ÿ) ► Image
-
-
0
6
0
-2
(-2)² = 4
3.6
3.62-7.2
1
2
1
2
-1
(−1)² = 1
-0.4
-1 -0.4 0.4
2
3
4
6
0
0² = 0
0.6
3
1
9
3
1
(1)² = 1
-1.4
4
0
16
0
2
(2)² = 4
-2.4
0.0.60
1.-1.4-1.4
22.44.8
Στι
ΣYi
Σα
ΣYixi Σ(xi) Image
Σ(α; - π)2
Σ(y: - 3)
-
Σ(xi — x) (Yi — ÿ)
10
12
30
11
10
0
-13
(a) Using the values above, calculate the estimates for the intercept 61 and slope 62.
(b) Using the numerical values above, show that
Σ(x − x)² =
-
x² – Nò and
Σ(xi - x) (yi – y) = Σ x iyi - Nx + y
XiYi
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