A study was conducted on time taken (in seconds) for an algorithm to finish running, y, and processing power of a machine, r. A linear model was fitted using the statistical software R, producing the following output: Coefficients: (Intercept) 98.81082 -0.75263 Estimate std. Error t value Pr(>It|) 3.31574 0.04277 29.8 1.74e-09 *** -17.6 1.1le-07 *** Signif. codes: 0 ***** 0.001 *** 0.01 *' 0.05 '.' 0.1''1 Residual standard error: 4.304 on 8 degrees of freedom Multiple R-squared: 0.9748, F-statistic: 309.7 on 1 and 8 DF, p-value: 1.1le-07 Adjusted R-squared: 0.9717 (a) From the R output, compute the sample corelation coefficient and interpret its value. (b) From the R output, obtain the equation of the estimated regression line. (c) Interpret the slope coefficient. (d) Discuss whether the simple linear regression model obtained does a good job of explaining observed variation in the time taken for an algorithm to finish running. (e) Using information from the R output, compute the sum of squared errors. Explain what the sum of squared errors means.

A study was conducted on time taken (in seconds) for an algorithm to finish running, y, and processing power of a machine, r. A linear model was fitted using the statistical software R, producing the following output: Coefficients: (Intercept) 98.81082 -0.75263 Estimate std. Error t value Pr(>It|) 3.31574 0.04277 29.8 1.74e-09 * -17.6 1.1le-07 * Signif. codes: 0 *** 0.001 * 0.01 *' 0.05 '.' 0.1''1 Residual standard error: 4.304 on 8 degrees of freedom Multiple R-squared: 0.9748, F-statistic: 309.7 on 1 and 8 DF, p-value: 1.1le-07 Adjusted R-squared: 0.9717 (a) From the R output, compute the sample corelation coefficient and interpret its value. (b) From the R output, obtain the equation of the estimated regression line. (c) Interpret the slope coefficient. (d) Discuss whether the simple linear regression model obtained does a good job of explaining observed variation in the time taken for an algorithm to finish running. (e) Using information from the R output, compute the sum of squared errors. Explain what the sum of squared errors means.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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