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Exercise 5: Regression Analysis - Fitting a Linear Regression Model and Hypothesis Testing, Assignments of Data Analysis & Statistical Methods

Millikin University (MU)Data Analysis & Statistical Methods
Prof. Eun-Joo Lee

The instructions and data for exercise 5 of ma 220, where students are required to fit a least squares line to a given dataset using the formula y = β0 + β1x + ε, calculate the sum of squared errors (sse), standard error (s2), and standard deviation (s. The exercise also includes hypothesis testing to determine if β1 is significantly different from zero or positive, and finding the 95% confidence interval for β1.

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Pre 2010

Uploaded on 08/04/2009

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MA 220 - 02
E. Lee
Exercise 5
1. Consider the model, y=β0+β1x+εand some preliminary calculations from a data set.
Σx= 45.12,Σy= 114.6,Σx2= 88.7788,Σy2= 575.02,Σxy = 225.04, n = 24
(a) Fit a least squares line to the data.
(b) Calculate SSE, s2and s.
pf2

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MA 220 - 02

E. Lee

Exercise 5

  1. Consider the model, y = β 0 + β 1 x + ε and some preliminary calculations from a data set. Σx = 45. 12 , Σy = 114. 6 , Σx^2 = 88. 7788 , Σy^2 = 575. 02 , Σxy = 225. 04 , n = 24 (a) Fit a least squares line to the data.

(b) Calculate SSE, s^2 and s.

MA 220 - 02

E. Lee

Exercise 5

(c) Test if β 1 6 = 0 using α =. 05

(d) Find the approximate p-value for the test and interpret its value.

(e) Find a 95% confidence interval for β 1.

  1. Consider the model, y = β 0 + β 1 x + ε and some preliminary calculations from a data set. Σx = 120, Σy =. 37 , Σxy = 3. 86 , Σx^2 = 1240, Σy^2 =. 0127 , n = 15 (a) Fit a least squares line to the data. (b) Calculate SSE, s^2 and s. (c) Test if β 1 > 0 using α =. 05

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