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Problem 7. deposition appeared in a recent study. The accompanying data on x = current density (mA/cm) and y = rate of 20 40 60 80 y .24 1.20 1.71 2.22 For the data: n = 4, E x¡ = 200, E y, = 5.37, Sxx = 2000, Sxy = 64.5, SSE = .06075, SST = Syy = 2.140875. a. Find b, (that is ß1). b. What is the equation of the regression line? c. Compute estimated o² (or s²).

Problem 7. deposition appeared in a recent study. The accompanying data on x = current density (mA/cm) and y = rate of 20 40 60 80 y .24 1.20 1.71 2.22 For the data: n = 4, E x¡ = 200, E y, = 5.37, Sxx = 2000, Sxy = 64.5, SSE = .06075, SST = Syy = 2.140875. a. Find b, (that is ß1). b. What is the equation of the regression line? c. Compute estimated o² (or s²).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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### Problem 7 The accompanying data on \( x = \) current density (mA/cm) and \( y = \) rate of deposition appeared in a recent study. | \( x \) | 20 | 40 | 60 | 80 | |--------|-----|-----|-----|-----| | \( y \) | 0.24 | 1.20 | 1.71 | 2.22 | For the data: \[ n = 4, \quad \sum{x_i} = 200, \quad \sum{y_i} = 5.37, \quad S_{xx} = 2000, \quad S_{xy} = 64.5, \quad SSE = 0.06075, \quad SST = S_{yy} = 2.140875. \] ### Questions: #### a. Find \( b_1 \) (that is \( \hat{\beta}_1 \)). #### b. What is the equation of the regression line? #### c. Compute the estimated \( \sigma^2 \) (or \( s^2 \)). #### d. Do you agree with the claim by the article's author that “a linear relationship was obtained from the tin-lead rate of deposition as a function of current density”? Explain your reasons. ### Graphs and Diagrams Explanation - There are no graphs or diagrams in this problem. The problem consists of a table of data and several statistical measures related to linear regression analysis. The table presents the values of current density (x) in mA/cm and the corresponding rate of deposition (y) in some unit. The provided statistics (such as \( S_{xx} \) and \( S_{xy} \)) are used for computing regression coefficients and other measures necessary for assessing the linear relationship. Make sure to use these statistics and the given formulas for your computations to answer questions (a) through (d).
Transcribed Image Text:### Problem 7 The accompanying data on \( x = \) current density (mA/cm) and \( y = \) rate of deposition appeared in a recent study. | \( x \) | 20 | 40 | 60 | 80 | |--------|-----|-----|-----|-----| | \( y \) | 0.24 | 1.20 | 1.71 | 2.22 | For the data: \[ n = 4, \quad \sum{x_i} = 200, \quad \sum{y_i} = 5.37, \quad S_{xx} = 2000, \quad S_{xy} = 64.5, \quad SSE = 0.06075, \quad SST = S_{yy} = 2.140875. \] ### Questions: #### a. Find \( b_1 \) (that is \( \hat{\beta}_1 \)). #### b. What is the equation of the regression line? #### c. Compute the estimated \( \sigma^2 \) (or \( s^2 \)). #### d. Do you agree with the claim by the article's author that “a linear relationship was obtained from the tin-lead rate of deposition as a function of current density”? Explain your reasons. ### Graphs and Diagrams Explanation - There are no graphs or diagrams in this problem. The problem consists of a table of data and several statistical measures related to linear regression analysis. The table presents the values of current density (x) in mA/cm and the corresponding rate of deposition (y) in some unit. The provided statistics (such as \( S_{xx} \) and \( S_{xy} \)) are used for computing regression coefficients and other measures necessary for assessing the linear relationship. Make sure to use these statistics and the given formulas for your computations to answer questions (a) through (d).
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