(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.

(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.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.6: Rational Functions

Problem 11SC: Find the mean hourly cost when the cell phone described above is used for 240 minutes.

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Question

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.

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