A researcher wants to know if the gestation period of an...

A researcher wants to know if the gestation period of an animal can be used to predict life expectancy. She collects the following data: CAN'T COPY THE TABLE (a) Suppose the researcher wants to use the gestation period of an animal to predict its life expectancy. Determine which variable is the explanatory variable and which is the response variable. (b) Draw a scatter diagram. (c) Compute the linear correlation coefficient between gestation period and life expectancy. (d) Comment on the type of relation that appears to exist between gestation period and life expectancy based on the scatter diagram and linear correlation coefficient. (c) Remove the goat from the data set, and recompute the linear correlation coefficient between the gestation period and life expectancy. What effect did the removal of the data value have on the linear correlation coefficient? Provide a justification for this result.

A researcher wants to know if the gestation period of an animal can be used to predict life expectancy. She collects the following data:
CAN'T COPY THE TABLE
(a) Suppose the researcher wants to use the gestation period of an animal to predict its life expectancy. Determine which variable is the explanatory variable and which is the response variable.
(b) Draw a scatter diagram.
(c) Compute the linear correlation coefficient between gestation period and life expectancy.
(d) Comment on the type of relation that appears to exist between gestation period and life expectancy based on the scatter diagram and linear correlation coefficient.
(c) Remove the goat from the data set, and recompute the linear correlation coefficient between the gestation period and life expectancy. What effect did the removal of the data value have on the linear correlation coefficient? Provide a justification for this result.

Key Concepts

Impact of Outliers

Outliers are data points that deviate markedly from the other observations and can significantly influence the results of a statistical analysis. In the context of correlation, the presence of an outlier may exaggerate or mask the true strength of the relationship between variables. Evaluating the effect of an outlier involves understanding how its inclusion or removal alters the linear correlation coefficient, thereby informing the robustness and reliability of the predictive model.

Linear Correlation Coefficient

The linear correlation coefficient, commonly denoted as r, quantifies the strength and direction of a linear relationship between two quantitative variables. With values ranging from -1 to 1, a value near 1 indicates a strong positive linear relationship, near -1 indicates a strong negative linear relationship, and around 0 suggests little or no linear association. This metric is essential for summarizing the linear dependence between variables.

Explanatory and Response Variables

This concept involves differentiating between the variable used to predict (explanatory or independent variable) and the variable that is being predicted (response or dependent variable). In prediction or regression analysis, identifying which variable is considered the predictor and which is the outcome is crucial for understanding the directionality of the relationship and setting up the analysis correctly.

Scatter Diagram

A scatter diagram, or scatter plot, is a graphical representation that uses dots to display the relationship between two quantitative variables. Each point represents an observation, with the independent variable typically plotted on the x-axis and the dependent variable on the y-axis. This visual tool helps in identifying patterns, trends, potential linear relationships, and unusual observations or outliers.

Transcript

00:01 All righty guys.

00:03 So for this problem here, we're going to go ahead and figure out which variable is the explanatory and which is the response.

00:12 So another way to figure out what explanatory and response are is explanatory happens first and response happens second.

00:21 So what happens first? justation period or life expectancy? well, gestation will happen before you die.

00:30 So it looks like gestation is our explanatory variable in this case.

00:34 So let's actually write down all of the days here.

00:47 This goes for x.

00:48 Remember, explanatory is x.

00:50 All response is y.

00:54 And there we go.

01:06 So those are x and y values.

01:08 So after i put those in, by putting these in, it makes it very easy for me to find the scatter diagram as well as the linear correlation coefficient.

01:18 All righty.

01:19 So let's go ahead and do that.

01:21 That.

01:22 Okay, so i'm going to find my scatter diagram.

01:26 I'm going to go out and highlight all the data.

01:28 And i do insert chart.

01:30 And there it is.

01:31 There is my data right there.

01:35 So, yeah, that is my scatter plot data.

01:38 And that will help me.

01:40 And so, yeah, that will help me kind of figure out, or kind of take a guess as well as to what all the values are.

01:47 So thinking about this, guys, i actually looking at this, i detect maybe a positive one.