The scatter plots show the results of a survey of 20...

The scatter plots show the results of a survey of 20 randomly selected males ages $24-35 .$ Using age as the explanatory variable, match each graph with the appropriate description. Explain your reasoning. (a) Age and body temperature (b) Age and balance on student loans (c) Age and income (d) Age and height (FIGURE CAN'T COPY)

The scatter plots show the results of a survey of 20 randomly selected males ages $24-35 .$ Using age as the explanatory variable, match each graph with the appropriate description. Explain your reasoning.
(a) Age and body temperature
(b) Age and balance on student loans
(c) Age and income
(d) Age and height
(FIGURE CAN'T COPY)

Key Concepts

Interpreting Graphical Data

Interpreting scatter plots involves evaluating the overall pattern and spread of the data points. Analysts consider the direction (upward or downward trend), form (linear or non-linear), strength (how closely the points fit a trend line), and the presence of any anomalies. This process is crucial for understanding how a variable like age might be associated with another variable such as income or height, based on expected real?world relationships.

Correlation and Trend Analysis

Correlation refers to the strength and direction of the linear relationship between the two variables depicted in a scatter plot. A strong positive correlation means as one variable increases, the other tends to increase, while a negative correlation means one variable tends to decrease as the other increases. Recognizing these patterns is key when matching graphs to descriptions based on the expected trends.

Explanatory and Response Variables

In studies that use scatter plots, variables are classified as either explanatory (independent) or response (dependent). The explanatory variable is believed to influence or predict changes in the response variable. In the given context, age is used as the explanatory variable, and the other variables (such as body temperature, balance on student loans, income, or height) are considered response variables.

Scatter Plots

Scatter plots are visual tools used to examine the relationship between two quantitative variables. By plotting one variable along the x?axis and the other along the y?axis, these graphs help detect patterns, trends, and potential correlations between the variables, as well as identify outliers or unusual data points.

Transcript

00:01 In this example, we are going through a series of graphs and trying to match them to their description.

00:05 So we're given these data points plotted, and all of these have age as the explanatory variable.

00:10 And what we're using here is a sample size of 20 people.

00:14 So we have 20 data points for each graph here, age is the explanatory variable, and we're given these measurements.

00:21 So two of which, 15 and 17, you can see, are measured in thousands of units, whereas 16 and 18 are measured in just units.

00:30 All right, so let's go ahead and start with graph 15 right here.

00:36 So we're looking at age as our explanatory variable measured in thousands of units.

00:39 So which description might match this? well, looking at our descriptions, which one might be in thousands of units.

00:45 So age and body temperature, it wouldn't make sense to measure body temperature in thousands of units.

00:50 So we can rule that out.

00:51 B, age and student loan balance.

00:55 That's possible.

00:55 Student loan balances are probably going to be measured in thousands.

00:58 So it could be that one.

00:59 And c right here, age and income.

01:01 Income, again, is probably going to be measured in thousands of units.

01:04 So it could be that one as well.

01:05 And d, we can rule that out because height is not going to be measured in thousands of units either.

01:09 It's probably going to be measured in inches.

01:11 So we're down to student loan balance and income.

01:15 So let's think this through.

01:15 So for 15, what we see is we have a relatively upward sloping pattern going on.

01:21 So it looks like we have relatively strong positive correlation.

01:24 And what we're likely to see as people are getting older as we go from being 26, a relatively low income or student loan balance to 34 having a relatively high income or student loan balance, which seems more likely...

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