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Consider the following data on the number of minutes (x) that 10 persons spent on social media during office hours and their productivity level (y): 10 29 54 63 70 76 88 91 108 118 Yi 92 72 59 50 49 48 38 25 14 9. 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(>|t|) 29.8 1.74e-09 *** -17.6 1.1le-07 *** 3.31574 0.04277 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: F-statistic: 309.7 on 1 and 8 DF, p-value: 1.1le-07 0.9748, Adjusted R-squared: 0.9717 (a) Obtain the equation of the estimated regression line. (b) Interpret the slope coefficient. (c) Discuss whether the simple linear regression model obtained does a good job of explaining observed variation in productivity level. (d) Perform a model utility test using o 0 01 Use an anpropriate P-value from the output

Consider the following data on the number of minutes (x) that 10 persons spent on social media during office hours and their productivity level (y): 10 29 54 63 70 76 88 91 108 118 Yi 92 72 59 50 49 48 38 25 14 9. 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(>|t|) 29.8 1.74e-09 *** -17.6 1.1le-07 *** 3.31574 0.04277 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: F-statistic: 309.7 on 1 and 8 DF, p-value: 1.1le-07 0.9748, Adjusted R-squared: 0.9717 (a) Obtain the equation of the estimated regression line. (b) Interpret the slope coefficient. (c) Discuss whether the simple linear regression model obtained does a good job of explaining observed variation in productivity level. (d) Perform a model utility test using o 0 01 Use an anpropriate P-value from the output

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Please solve only part d) and part e)

Consider the following data on the number of minutes (x) that 10 persons spent on social media during office hours and their productivity level (y): Xi 10 29 54 63 70 76 88 91 108 118 Yi 92 72 59 50 49 48 38 25 14 9 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(>|t|) 29.8 1.74e-09 *** -17.6 1.1le-07 *** 3.31574 0.04277 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, Adjusted R-squared: p-value: 1.11e-07 0.9717 (a) Obtain the equation of the estimated regression line. (b) Interpret the slope coefficient. (c) Discuss whether the simple linear regression model obtained does a good job of explaining observed variation in productivity level. (d) Perform a model utility test using a = 0.01. Use an appropriate P-value from the output given. (Note: R uses the E notation to display very large or very small numbers. For example, 3.2e-4 = 3.25 x 10-4 = 0.000325.) (e) The R output provides a residual standard error of 4.304, and an estimated standard error value of 0.04277 for the slope coefficient. Provide the formulas used to obtain these two values, and describe what these standard errors are.
Transcribed Image Text:Consider the following data on the number of minutes (x) that 10 persons spent on social media during office hours and their productivity level (y): Xi 10 29 54 63 70 76 88 91 108 118 Yi 92 72 59 50 49 48 38 25 14 9 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(>|t|) 29.8 1.74e-09 *** -17.6 1.1le-07 *** 3.31574 0.04277 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, Adjusted R-squared: p-value: 1.11e-07 0.9717 (a) Obtain the equation of the estimated regression line. (b) Interpret the slope coefficient. (c) Discuss whether the simple linear regression model obtained does a good job of explaining observed variation in productivity level. (d) Perform a model utility test using a = 0.01. Use an appropriate P-value from the output given. (Note: R uses the E notation to display very large or very small numbers. For example, 3.2e-4 = 3.25 x 10-4 = 0.000325.) (e) The R output provides a residual standard error of 4.304, and an estimated standard error value of 0.04277 for the slope coefficient. Provide the formulas used to obtain these two values, and describe what these standard errors are.
а. The regression equation is as follows: y = 98.81082 –0.75263x Step 3 b. From the regression equation, the intercept is 98.81, and the slope of the regression equation-0.75. Here, the dependent variable is the productivity level and the independent variable is the time spend on social media. Thus, as the time spend on social media during office hours increases by a minute, the productivity level is expected to decrease by 0.75 units. For every one-minute increase in usage the productivity level decreases by 0.75 units. C. The value of R-squared is 0.9748. Hence, about 97% of the variation in the dependent variable, productivity level is explained by the independent variable, the number of minutes spent on social media. Hence, the simple linear regression model obtained does a good job of explaining observed variation in productivity level.
Transcribed Image Text:а. The regression equation is as follows: y = 98.81082 –0.75263x Step 3 b. From the regression equation, the intercept is 98.81, and the slope of the regression equation-0.75. Here, the dependent variable is the productivity level and the independent variable is the time spend on social media. Thus, as the time spend on social media during office hours increases by a minute, the productivity level is expected to decrease by 0.75 units. For every one-minute increase in usage the productivity level decreases by 0.75 units. C. The value of R-squared is 0.9748. Hence, about 97% of the variation in the dependent variable, productivity level is explained by the independent variable, the number of minutes spent on social media. Hence, the simple linear regression model obtained does a good job of explaining observed variation in productivity level.
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