Regression methods were used to analyze the data from a study investigating the lationship between compressive strength (x) and intrinsic permeability (y) of various oncrete mixes and cures. Summary quantities were n=20, E y;-572, E y?=23,530, x;=43, Ex?=157.42 and E x; y;=1697.80. ) Calculate the least squares estimates of the slope and intercept. -) Estimate o?. ) Suppose that the observed value of permeability at x=3.5 is y=41. Calculate the value the corresponding residual. Consider the following computer output: nalysis of Variance Source df SS MS F n-value

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1. Regression methods were used to analyze the data from a study investigating the
relationship between compressive strength (x) and intrinsic permeability (y) of various
concrete mixes and cures. Summary quantities were n=20, E y=572, E y}=23,530,
Σχ-43, Σx=157.42 and Σ x γι-1 697.80.
(a) Calculate the least squares estimates of the slope and intercept.
(b) Estimate o?.
(c) Suppose that the observed value of permeability at x=3.5 is y=41. Calculate the value
of the corresponding residual.
2. Consider the following computer output:
Analysis of Variance
Source
df SS
MS F p-value
Regression
1
Residual error
1404
Total
19 1500
a) Find the degree of freedom for the residual error.
b) What is the estimate of o??
c) Calculate the F-statistic value for the regression.
d) Estimate the p-value for the regression F-statistic.
Transcribed Image Text:1. Regression methods were used to analyze the data from a study investigating the relationship between compressive strength (x) and intrinsic permeability (y) of various concrete mixes and cures. Summary quantities were n=20, E y=572, E y}=23,530, Σχ-43, Σx=157.42 and Σ x γι-1 697.80. (a) Calculate the least squares estimates of the slope and intercept. (b) Estimate o?. (c) Suppose that the observed value of permeability at x=3.5 is y=41. Calculate the value of the corresponding residual. 2. Consider the following computer output: Analysis of Variance Source df SS MS F p-value Regression 1 Residual error 1404 Total 19 1500 a) Find the degree of freedom for the residual error. b) What is the estimate of o?? c) Calculate the F-statistic value for the regression. d) Estimate the p-value for the regression F-statistic.
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