An engineer wanted to determine how the weight of a car...

An engineer wanted to determine how the weight of a car affects gas mileage. The following data represent the weight of various domestic cars and their gas mileage in the city for the 2005 model year. CAN'T COPY THE TABLE (a) Determine which variable is the likely explanatory variable and which is the likely response variable. (b) Draw a scatter diagram of the data. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon in the city. (d) Comment on the type of relation that appears to exist between the weight of a car and its miles per gallon in the city based on the scatter diagram and the linear correlation coefficient.

An engineer wanted to determine how the weight of a car affects gas mileage. The following data represent the weight of various domestic cars and their gas mileage in the city for the 2005 model year.
CAN'T COPY THE TABLE
(a) Determine which variable is the likely explanatory variable and which is the likely response variable.
(b) Draw a scatter diagram of the data.
(c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon in the city.
(d) Comment on the type of relation that appears to exist between the weight of a car and its miles per gallon in the city based on the scatter diagram and the linear correlation coefficient.

Key Concepts

Interpretation of Relationship

Interpreting the relationship between two variables involves analyzing both the scatter diagram and the correlation coefficient to draw conclusions about the nature of their association. This includes determining whether the relationship is linear, assessing its strength and direction, and considering the potential implications or underlying causal factors driving the observed pattern.

Linear Correlation Coefficient

The linear correlation coefficient is a numerical measure that quantifies the strength and direction of a linear relationship between two quantitative variables. Typically represented by 'r', it varies between -1 and 1, where values close to 1 or -1 indicate a strong linear relationship, and values near 0 suggest a weak or no linear association.

Explanatory Variable

An explanatory variable, sometimes called the independent variable, is the variable that is presumed to influence or predict the outcome. In investigations, it is the factor that may have a causal relationship with the response variable, and it is typically manipulated or observed to understand its effect on another variable.

Response Variable

The response variable, also known as the dependent variable, is the outcome or variable that is being studied and measured to see how it is affected by changes in the explanatory variable. It reflects the results or effects in a study and is usually the focus of interest in understanding how it responds to different conditions.

Scatter Diagram

A scatter diagram, or scatter plot, is a graphical representation of the relationship between two quantitative variables. Each point on the plot corresponds to one observation, with one variable plotted along the horizontal axis and the other along the vertical axis, making it easy to visually assess patterns, trends, or potential correlations between the variables.

Transcript

00:01 All righty guys, so here we go.

00:03 The first thing we have to do is we have to figure out what is the explanatory and what's the response.

00:07 An easy way to figure out what's explanatory and what's response is to figure out what happens first, okay, so that we have weight and then gas usage.

00:17 So what's going to happen first? is the car get weight first or is the car used gas first? now obviously the cars be made and of course one of the cars made it's a certain weight.

00:25 So yeah.

00:27 And so since the weight happens first, weight will be our explanatory for x.

00:31 And then our y response variable will be miles per gallon.

00:35 Okay, so the first thing we need to do, at least for part b, is to make a scatter diagram.

00:41 So i went ahead and took the liberty of inputting all these values into a google sheet.

00:46 You can do the same thing for yourself as well.

00:48 And after that, i'm going to do insert chart.

00:51 And there it is.

00:52 There is my chart of my x and y values.

00:55 Okay.

00:57 So there it goes.

00:58 So this is a scatter chart here, by the way.

01:00 If it shows up like a histogram for you or something like that, if you click on something else, it will show up as a chart if you go under setup and then scatter chart.

01:09 And again, you get to this menu by hitting the edit chart.

01:12 You hit the three dots neighbor right, edit chart, and it'll take you to this menu.

01:16 And so there is your scatter plot...

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