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Chapter 13: Problem 16

Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression line for the given points. $$ (1,0),(3,3),(5,6) $$

Short Answer

Expert verified
The specific output will depend on the software used, so there isn't a specific 'correct' answer. The least squares regression line will be in the form \(y = mx + b\), where \(m\) and \(b\) are calculated by the software.

Step by step solution

01

Identification of Data Points

Firstly, identify the data points which are (1,0),(3,3),(5,6).
02

Input Data Points into Software

Secondly, enter these points into the desired software. In a spreadsheet, this would typically involve creating two columns - one for the x-values and one for the y-values.
03

Perform Regression Analysis

Thirdly, use the software to perform a regression analysis. In a spreadsheet, look for a function like 'LINEST' (in Excel) or 'LINEAR REGRESSION' (in Google Sheets).
04

Interpret the Output

Finally, interpret the output. The software will provide you with an equation in the form \(y = mx + b\), where \(m\) is the slope of the line and \(b\) is the y-intercept.

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Most popular questions from this chapter

The global numbers of personal computers \(x\) (in millions) and Internet users \(y\) (in millions) from 1999 through 2005 are shown in the table. $$ \begin{aligned} &\begin{array}{|l|c|c|c|c|} \hline \text { Year } & 1999 & 2000 & 2001 & 2002 \\ \hline \text { Personal computers, } x & 394.1 & 465.4 & 526.7 & 575.5 \\ \hline \text { Internet users, } y & 275.5 & 390.3 & 489.9 & 618.4 \\ \hline \end{array}\\\ &\begin{array}{|l|c|c|c|} \hline \text { Year } & 2003 & 2004 & 2005 \\ \hline \text { Personal computers, } x & 636.6 & 776.6 & 808.7 \\ \hline \text { Internet users, } y & 718.8 & 851.8 & 982.5 \\ \hline \end{array} \end{aligned} $$ (a) Use a graphing utility or a spreadsheet to create a scatter plot of the data. (b) Use the regression capabilities of a graphing utility or a spreadsheet to find an appropriate model for the data. (c) Explain why you chose the type of model that you created in part (b).

Use a symbolic integration utility to evaluate the double integral. $$ \int_{1}^{2} \int_{y}^{2 y} \ln (x+y) d x d y $$

Evaluate the double integral. $$ \int_{0}^{2} \int_{3 y^{2}-6 y}^{2 y-y^{2}} 3 y d x d y $$

Plot the points and determine whether the data have positive, negative, or no linear correlation (see figures below). Then use a graphing utility to find the value of \(r\) and confirm your result. The number \(r\) is called the correlation coefficient. It is a measure of how well the model fits the data. Correlation coefficients vary between \(-1\) and 1, and the closer \(|r|\) is to 1, the better the model. $$ (0.5,9),(1,8.5),(1.5,7),(2,5.5),(2.5,5),(3,3.5) $$

Use a double integral to find the volume of the solid bounded by the graphs of the equations. $$ z=x y, z=0, y=0, y=4, x=0, x=1 $$
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