The following table shows the number of fiber optic cable connections to homes in a country from 2000 to 2004 (t = 0 represents 2000). Year t o 1 2 3 4 Connections c s15 3o 70 155 (Thousands) (a) Use technology to obtain the linear regression line and the correlation coefficient r, with all coefficients rounded to two decimal places. c(t) = Plot the regression line and the given points. 100 100 (b) Does the graph suggest that a nonlinear relationship between t and c would be more appropriate than a linear one? Why? Yes, the first and last points lie above the regression line, while the central points lie below it, suggesting a nonlinear relationship. No, the points appear to be randomly scattered about the regression line which does not imply a nonlinear relationship. (C) Use technology to obtain the residuals. (Round your answers to two decimal places.) Year t Residual 1 2 3 4 What can you say about the residuals in support of the claim in part (b)? The residuals vary from positive to negative with no observable pattern, confirming the impression from the graph. The residuals are positive at first, become negative, and then become positive, confirming the impression from the graph.

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The following table shows the number of fiber optic cable connections to homes in a country from 2000 to 2004 (t = 0 represents 2000).
Year t o 1 2 3 4
Connections c s15 3o 70 155
(Thousands)
(a) Use technology to obtain the linear regression line and the correlation coefficient r, with all coefficients rounded to two decimal places.
c(t) =
Plot the regression line and the given points.
100
100
(b) Does the graph suggest that a nonlinear relationship between t and c would be more appropriate than a linear one? Why?
Yes, the first and last points lie above the regression line, while the central points lie below it, suggesting a nonlinear relationship.
No, the points appear to be randomly scattered about the regression line which does not imply a nonlinear relationship.
(C) Use technology to obtain the residuals. (Round your answers to two decimal places.)
Year t Residual
1
2
3
4
What can you say about the residuals in support of the claim in part (b)?
The residuals vary from positive to negative with no observable pattern, confirming the impression from the graph.
The residuals are positive at first, become negative, and then become positive, confirming the impression from the graph.
Transcribed Image Text:The following table shows the number of fiber optic cable connections to homes in a country from 2000 to 2004 (t = 0 represents 2000). Year t o 1 2 3 4 Connections c s15 3o 70 155 (Thousands) (a) Use technology to obtain the linear regression line and the correlation coefficient r, with all coefficients rounded to two decimal places. c(t) = Plot the regression line and the given points. 100 100 (b) Does the graph suggest that a nonlinear relationship between t and c would be more appropriate than a linear one? Why? Yes, the first and last points lie above the regression line, while the central points lie below it, suggesting a nonlinear relationship. No, the points appear to be randomly scattered about the regression line which does not imply a nonlinear relationship. (C) Use technology to obtain the residuals. (Round your answers to two decimal places.) Year t Residual 1 2 3 4 What can you say about the residuals in support of the claim in part (b)? The residuals vary from positive to negative with no observable pattern, confirming the impression from the graph. The residuals are positive at first, become negative, and then become positive, confirming the impression from the graph.
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