Lines of Best Fit

Then the data values are written in the columns.

By pressing the $\boxed{\text{STAT}}$ button and then selecting the CALC menu, the option LinReg($ax+b$) can be found. This option gives the line of best fit, expressed as a linear function in slope-intercept form.

Rounding the values of $a$ and $b$ to two decimal places, the equation of the line of best fit can be written as follows. The correlation coefficient is the value of $r$ on the screen. The value of $r$ varies from $\text{-}1$ to $1.$ A value close to $\text{-}1$ indicates a negative correlation, while a value close to $1$ indicates a positive correlation. Since the correlation coefficient is close to $1,$ the data has a strong positive correlation.

Then, to graph the scatter plot push the buttons $\boxed{\text{2nd}}$ and $\boxed{\text{Y=}}.$ Choose one of the plots in the list. Select the option ON, choose the type to be a scatter plot, and assign ${\text{L}}_1$ and ${\text{L}}_2$ as XList and Ylist, respectively.

The plot can be made by pressing the button $\boxed{\text{GRAPH}}.$ It is possible that after drawing the plot the window-size is not adequate for seeing all the information.

To fix this press $\boxed{\text{ZOOM}}$ and select the option ZoomStat. After doing so the window will resize to show the important information.

In this equation, the slope is $0.55$ and the $y\text{-}$intercept is $4.74.$

• The slope indicates that for every centimeter that the tree grows in diameter, about $0.55$ meters are gained in height.
• The $y\text{-}$intercept indicates that the minimum height for which this equation is valid is about $4.74$ meters. This can be because the diameter at chest height is not a good measure for smaller trees.

Then the data values can be written in the columns.

Finally, by pressing the $\boxed{\text{STAT}}$ button and then selecting the menu item CALC, the option LinReg($ax+b$) can be found. This option gives a line of best fit, expressed as a linear function in slope-intercept form.

Rounding to two decimal places, the equation for the line of best fit using linear regression can be written as follows. The correlation coefficient is the value of $r$ on the screen. The value of $r$ varies from $\text{-}1$ to $1.$ A value close to $\text{-}1$ indicates a negative correlation, while a value close to $1$ indicates a positive correlation. Since the value is almost $\text{-}1,$ the data have a very strong negative correlation.

To graph the scatter plot, first push the buttons $\boxed{\text{2nd}}$ and $\boxed{\text{Y=}}.$ Then, choose one of the plots in the list. Select the option ON, choose the type to be a scatter plot, and assign ${\text{L}}_1$ and ${\text{L}}_2$ as XList and Ylist, respectively.

The plot can be made by pressing the button $\boxed{\text{GRAPH}}.$ It is possible that after drawing the plot the window-size is not large enough to see all of the information.

To fix this, press $\boxed{\text{ZOOM}}$ and select the option ZoomStat. After doing that, the window will resize to show the important information.

In this equation, the slope is $\text{-}0.50$ and the $y\text{-}$intercept is $14.71.$

• The slope indicates that every one thousand feet of altitude, the pressure diminishes by about $0.50$ PSI.
• The $y\text{-}$intercept indicates that the pressure at sea level is about $14.71$ PSI.

To find the value of $y$ when $x=6,$ press $\boxed{\text{CALC}}$ ($\boxed{\text{2ND}}$ and $\boxed{\text{TRACE}}).$ Then press $\boxed{\text{ENTER}}$ to insert the value of $6$ for $x.$ Finally, press $\boxed{\text{ENTER}}$ again.

The value of the pressure at $6000$ feet is about $11.7$ PSI. Since all the data values are close to the line of best fit and the data is strongly correlated, it can be said that this is a good approximation of the actual value.

Solving Using the Equation

This prediction can also be found by substituting $6$ for $x$ into the equation for the line of best fit.

The data values can be written in the columns.

Finally, by pressing the $\boxed{\text{STAT}}$ button and then selecting the menu item CALC, the option LinReg($ax+b$) can be found. This option gives a line of best fit, expressed as a linear function in slope-intercept form.

Rounding to two decimal places, the equation for the line of best fit using linear regression can be written as follows. It should be noted that in this equation $x$ is the number of the exercise and $y$ is the time in minutes in which Davontay completed that exercise. The correlation coefficient is the value of $r$ on the screen. The value of $r$ varies from $\text{-}1$ to $1.$ A value close to $\text{-}1$ indicates a negative correlation, while a value close to $1$ indicates a positive correlation. But the value of $r$ is close to $0,$ this means that the data have no correlation.

To graph the scatter plot, first push the buttons $\boxed{\text{2nd}}$ and $\boxed{\text{Y=}}.$ Then, choose one of the plots in the list. Select the option ON, choose the type to be a scatter plot, and assign ${\text{L}}_1$ and ${\text{L}}_2$ as XList and Ylist, respectively.

The plot can be made by pressing the button $\boxed{\text{GRAPH}}.$ It is possible that after drawing the plot the window-size is not large enough to see all of the information.

To fix this, press $\boxed{\text{ZOOM}}$ and select the option ZoomStat. After doing that, the window will resize to show the important information.

Looking at the graph, it can be seen that the line of best fit is not close to any of the provided data points.

In this equation, the slope is $0.14$ and the $y\text{-}$intercept is $9.43.$

• The slope indicates that after every exercise, the next one takes about an additional $0.14$ minutes to complete.
• The $y\text{-}$intercept indicates that the minimum time to complete an exercise is about $9.43$ minutes.

From Part C it can be noted that the line is not representative of the given data points. This means that these measures do not reflect the reality of the exercises.

Then, to find the value of $y$ when $x=8,$ press $\boxed{\text{CALC}}$ ($\boxed{\text{2ND}}$ and $\boxed{\text{TRACE}}).$ Then press $\boxed{\text{ENTER}}$ to insert the value of $8$ for $x.$ Finally, press $\boxed{\text{ENTER}}$ again.

The value of $y$ when $x=8$ is about $10.57.$ This means that Davontay will finish the eighth exercise in less than $11$ minutes. Since none of the given data values are really close to the line of best fit and the data is not correlated, it can be said that this is a not good approximation for the actual value.

Solving Using the Equation of the Line of Best Fit

This prediction can also be found by substituting $8$ for $x$ into the equation for the line of best fit.