Question

The table shows the highest maximum temperature for the month of October in Philadelphia Pennsylvania over the yearsPart A identify the independent and dependent quantity in their units of measure?Part B identify the equation of line of best fit using the data table.what is the slope and y-intercept of the line and what do they represent?

Answer 1

Answers:

A. Independent = Year

Dependent = Temperature

B. Temp = 0.6733(Year) - 1293.61

Step-by-step explanation:

The independent variable is the variable that is not affected by the other, in this case, no matter the temperature, the year is given, so the independent variable is the year and the dependent variable is the highest temperature because it changes depending on the year.

Then, to identify the equation of the line of best fit, we will use the following:

First, we need to calculate the mean of both variables, so:

`\begin{gathered} \text{Mean Year = }(2008+2009+2010+2011+2012+\cdots+2017)/(10) \\ \text{Mean Year = }2012.5 \\ \text{Mean Temperature = }(64.9+53.1+61+54+\cdots+66.9)/(10) \\ \text{Mean Temperature=}61.47 \end{gathered}`

Then, we need to fill the following table:

Now, the slope of the line can be calculated as the sum of the values in the row (Year - Mean Year) x (Temp - Mean Temp) divided by the sum of the row (Year - Mean Year)^2. So, the slope of the line is:

`m=(55.55)/(82.5)=0.6733`

Finally, the y-intercept can be calculated as:

`\begin{gathered} b=\text{Temp Mean - Slope x Year Mean} \\ b=61.47-0.6733(2012.5) \\ b=-1293.61 \end{gathered}`

So, the equation of the line that best fits the data table is:

`\text{Temp}=0.6733(\text{Year)}-1293.61`