Question1. Construct a scatter diagram of the two variables, placing GNP per capita (in s) on the X -axis and willing to pay more for environmental protection on the Y -axis.
2. The correlation coefficient is .365 . What does this tell you about the relationship between the two variables?
3. The regression equation for this data provides us with the following results:
Interpret this equation. What do the intercept and slope tell you about the relationship between the two variables? What else can you report about these results?
Studdy Solution
STEP 1
What is this asking?
We're exploring how a country's wealth (GNP per capita) relates to its citizens' willingness to pay for environmental protection, using a scatter plot, correlation, and a regression equation.
Watch out!
Correlation doesn't imply causation!
Just because wealth and environmental concern seem linked doesn't mean one *causes* the other.
There could be other factors at play!
STEP 2
1. Create the scatter plot
2. Interpret the correlation coefficient
3. Interpret the regression equation
STEP 3
We'll **plot** each country's data point on a graph.
The x-coordinate is the GNP per capita (in s), and the y-coordinate is the percentage of people willing to pay more for environmental protection.
Imagine each country as a dot on our graph!
STEP 4
The **correlation coefficient**, \(0.365\), tells us about the *strength* and *direction* of the linear relationship between the two variables.
STEP 5
Since it's **positive**, it means that as GNP per capita *increases*, the willingness to pay for environmental protection *tends* to increase too.
They move in the same direction!
STEP 6
A correlation of \(0.365\) suggests a *moderate*, positive relationship.
It's not super strong, but it's definitely there.
STEP 7
Our regression equation is \(Y = 49.19 + 0.59X\).
This equation helps us *predict* the percentage of people willing to pay more for environmental protection () based on a country's GNP per capita ().
STEP 8
The **intercept**, \(49.19\), represents the predicted percentage willing to pay more when the GNP per capita is .
In other words, even in a country with *zero* GNP per capita, we predict about \(49.19\%\) of people would still be willing to pay more for environmental protection.
STEP 9
The **slope**, \(0.59\), tells us how much the predicted percentage willing to pay more *changes* for every increase in GNP per capita.
So, for every increase in GNP per capita, the predicted percentage willing to pay more goes up by \(0.59\%\)!
STEP 10
The p-value, \(P < 0.01\), tells us that this relationship is statistically significant.
It means it's very unlikely we'd see a relationship this strong by chance alone.
Our findings are likely real and not just a fluke!
STEP 11
The scatter plot visually represents the relationship between GNP per capita and willingness to pay for environmental protection.
The correlation coefficient of \(0.365\) indicates a moderate, positive linear relationship.
The regression equation, \(Y = 49.19 + 0.59X\), allows us to predict willingness to pay based on GNP per capita, with the intercept (\(49.19\)) representing the predicted percentage at zero GNP per capita and the slope (\(0.59\)) indicating the change in percentage for every increase in GNP per capita.
The p-value (\) confirms the statistical significance of the relationship.
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