[Table] A real-estate agent is trying to determine the relationship between the distance a 3-bedroom home is from New York City and its average selling price. He records the data for 6 homes shown below. Linear or Quadratic? Equation: Approximate cost of home 90 miles from NYC?

Question
Linear equations and graphs
asked 2021-02-09
[Table]
A real-estate agent is trying to determine the relationship between the distance a 3-bedroom home is from New York City and its average selling price. He records the data for 6 homes shown below.
Linear or Quadratic?
Equation:
Approximate cost of home 90 miles from NYC?

Answers (1)

2021-02-10
Input the x-values under L1 in a graphing calculator and the yy-values, in thousands, under L2 (for example, input 755,000 as 755). Then graph the scatterplot to determine if it's linear or quadratic:
[Graph]
The points approximately lie on a straight line so the data is linear.
Use the LinReg feature on your graphing calculator to find the values of aa and bb for the line of best fit:
[Graph]
Since a≈−4.3 and b≈795.6, the equation is y=−4.3x+795.6.
If a home is x=90 miles from NYC, then y=−4.3(90)+795.6=408.6≈409 (round to the nearest whole number since the costs in the table are rounded to the nearest thousand). The cost of the home is then about $409,000
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Relevant Questions

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True or False
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\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{l}\right|}{l}{\left|{l}\right|}\right\rbrace}{h}{l}\in{e}\text{Blend}&\text{Mix requirement}&\text{Selling price/lb(\\$)}\backslash{h}{l}\in{e}\text{special}&\text{at least 40% columbian,}&{6.50}\backslash&\text{at least 30% mocha}\backslash{h}{l}\in{e}\text{Dartk}&\text{at least 60% Brazillian}&{5.25}\backslash&\text{no more than 10% mid}\backslash{h}{l}\in{e}\text{Regular}&\text{no more than 60% mid}&{3.75}\backslash&\text{at least 30% Brazillian}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
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Two scatterplots are shown below.
Scatterplot 1
A scatterplot has 14 points.
The horizontal axis is labeled "x" and has values from 30 to 110.
The vertical axis is labeled "y" and has values from 30 to 110.
The points are plotted from approximately (55, 60) up and right to approximately (95, 85).
The points are somewhat scattered.
Scatterplot 2
A scatterplot has 10 points.
The horizontal axis is labeled "x" and has values from 30 to 110.
The vertical axis is labeled "y" and has values from 30 to 110.
The points are plotted from approximately (55, 55) steeply up and right to approximately (70, 90), and then steeply down and right to approximately (85, 60).
The points are somewhat scattered.
Explain why it makes sense to use the least-squares line to summarize the relationship between x and y for one of these data sets but not the other.
Scatterplot 1 seems to show a relationship between x and y, while Scatterplot 2 shows a relationship between the two variables. So it makes sense to use the least squares line to summarize the relationship between x and y for the data set in , but not for the data set in .
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