2. (Problem 11.2.3) An article in Concrete Research presented data on compressive strength x and intrinsic permeability y of various concrete mixes and cures. Summary quantities are n = 14, ? yi = 572, ? yi² = 23530, ? xi = 43, ? xi² = 157.42 and ? xiyi = 1697.80. Assume that the two variables are related according to the simple linear regression model. a. Calculate the least squares estimates of the slope and intercept. Estimate ?². b. Use the equation of the fitted line to predict what permeability would be observed when the compressive strength is x=4.3. c. Give a point estimate of the mean permeability when the compressive strength is x=3.7. d. Suppose that the observed value of permeability at x = 3.7 is y = 46.1. Calculate the value of the corresponding residual.
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To calculate the least squares estimates of the slope (b1) and intercept (b0), we can use the following formulas: b1 = (Σxiyi - (Σxi)(Σyi)/n) / (Σxi^2 - (Σxi)^2/n) b0 = (Σyi - b1(Σxi))/n Plugging in the given values: b1 = (1697.80 - (43)(572)/14) / (157.42 - Show more…
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An article in Concrete Research ["Near Surface Characteristics of Concrete: Intrinsic Permeability" (Vol. 41 , 1989 ) ] presented data on compressive strength $x$ and intrinsic permeability $y$ of various concrete mixes and cures. Summary quantities are $n=14, \sum y_{i}=572, \Sigma y_{i}^{2}=23,530, \sum x_{i}=43, \sum x_{i}^{2}=$ $157.42,$ and $\sum x_{i} y_{i}=1697.80 .$ Assume that the two variables are related according to the simple linear regression model. (a) Calculate the least squares estimates of the slope and intercept. Estimate $\sigma^{2}$. Graph the regression line. (b) Use the equation of the fitted line to predict what permeability would be observed when the compressive strength is $x=4.3$ (c) Give a point estimate of the mean permeability when compressive strength is $x=3.7$ (d) Suppose that the observed value of permeability at $x=$ 3.7 is $y=46.1 .$ Calculate the value of the corresponding residual.
Simple Linear Regression and Correlation
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An article in a concrete research presented data on compressive strength x and intrinsic permeability y of various concrete mixes and cures. Summary quantities are: n = 14, Ly = 572, yt = 23,530, Xi = 43, Lx = 157.42, and XiYi = 1697.80. Assume that the two variables are related according to the simple linear regression model. Calculate the least squares estimates of the slope. Calculate the least squares estimates of the intercept. Use the equation of the fitted line to predict what permeability would be observed when the compressive strength is x = 4.3.
Shaiju T.
An article in Concrete Research ("Near Surface Characteristics of Concrete: Intrinsic Permeability," Vol. 41, 1989), presented data on compressive strength x and intrinsic permeability y of various concrete mixes and cures. Summary quantities are n = 14, ∑ yဢ = 572, ∑ yဢ² = 23530, ∑ xဢ = 43, ∑ xဢ² = 157.42, and ∑ xဢyဢ = 1697.80. Assume that the two variables are related according to the simple linear regression model. Round your answers to 2 decimal places. Find a 90.0% confidence interval on each of the following: (a) Intercept. (b) Slope. (c) Mean permeability when x = 3.4. (d) Find a 90.0% prediction interval on permeability when x = 3.4.
Sri K.
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