Research performed at NASA and led by Emily R. Morey-Holton...

Research performed at NASA and led by Emily R. Morey-Holton measured the lengths of the right humerus and right tibia in 11 rats that were sent to space on Spacelab Life Sciences $2 .$ The following data were collected. CAN'T COPY THE TABLE (a) Draw a scatter diagram, treating the length of the right humerus as the explanatory variable and the length of the right tibia as the response variable. (b) Compute the linear correlation coefficient between the length of the right humerus and the length of the right tibia. (c) Comment on the type of relation that appears to exist between the length of the right humerus and the length of the right tibia based on the scatter diagram and the linear correlation coefficient. (d) Convert the data to inches $(1 \mathrm{mm}=0.03937 \text { inch })$ and recompute the linear correlation coefficient. What effect did the conversion from millimeters to inches have on the linear correlation coefficient?

Research performed at NASA and led by Emily R. Morey-Holton measured the lengths of the right humerus and right tibia in 11 rats that were sent to space on Spacelab Life Sciences $2 .$ The following data were collected.
CAN'T COPY THE TABLE
(a) Draw a scatter diagram, treating the length of the right humerus as the explanatory variable and the length of the right tibia as the response variable.
(b) Compute the linear correlation coefficient between the length of the right humerus and the length of the right tibia.
(c) Comment on the type of relation that appears to exist between the length of the right humerus and the length of the right tibia based on the scatter diagram and the linear correlation coefficient.
(d) Convert the data to inches $(1 \mathrm{mm}=0.03937 \text { inch })$ and recompute the linear correlation coefficient. What effect did the conversion from millimeters to inches have on the linear correlation coefficient?

Key Concepts

Linear Correlation Coefficient

The linear correlation coefficient is a statistical measure that quantifies the strength and direction of a linear relationship between two variables. Its value ranges from -1 to 1, where values close to 1 indicate a strong positive linear association, values close to -1 indicate a strong negative linear relationship, and values near 0 suggest little or no linear correlation.

Effect of Unit Conversion on the Correlation Coefficient

When data are converted using a linear transformation, such as converting measurements from millimeters to inches, the correlation coefficient remains unchanged. This is because the measure is scale invariant; linear conversion factors do not affect the standardized relationship between the variables.

Scatter Diagram

A scatter diagram is a graphical representation of two quantitative variables where each point represents an observation based on its values for the two variables. It is used to visually assess the pattern or relationship between the explanatory and response variables, such as identifying trends, clusters, or potential outliers.

Explanatory and Response Variables

In data analysis, the explanatory variable (also called the independent variable) is the one thought to be influencing or predicting the response variable (dependent variable), which is the outcome of interest. Distinguishing these variables is key in regression analysis, as it defines the direction of the analysis and interpretation of the relationship.

Transcript

Please give Ace some feedback