When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations. 

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x or y variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

First, let’s observe if we can make a prediction using the following data:

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 185 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 185 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

From this information, we can make the prediction that a male of this weight should be able to run a mile in just under ten minutes.

Now, lets predict this value quantitatively using the equation of the line:

$\displaystyle y=0.0824x-5.5299$

Plug in 185 for the x-coordinate.

$\displaystyle y=0.0824(185)-5.5299$

Solve.

$\displaystyle y=15.244-5.5299$

$\displaystyle y=9.7141$

Round to two decimal places.

$\displaystyle y=9.71$

According to the data, we can predict that it would take a male 9.71 minutes for a 185 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations. 

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 185 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 185 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

From this information, we can make the prediction that a male of this weight should be able to run a mile in just under ten minutes.

Now, lets predict this value quantitatively using the equation of the line:

$\displaystyle y=0.0824x-5.5299$

Plug in 185 for the x-coordinate.

$\displaystyle y=0.0824(185)-5.5299$

Solve.

$\displaystyle y=15.244-5.5299$

$\displaystyle y=9.7141$

Round to two decimal places.

$\displaystyle y=9.71$

According to the data, we can predict that it would take a male 9.71 minutes for a 185 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.