Calculate the correlation coefficient for the following heights of fathers (X) and their sons (Y): X (inches) 65 66 67 67 68 69 70 72 Y (inches) 67 68 65 68 72 72 69 71
Added by Timothy S.
Step 1
For X: \[ \bar{X} = \frac{65 + 66 + 67 + 67 + 68 + 69 + 70 + 72}{8} = \frac{544}{8} = 68 \] For Y: \[ \bar{Y} = \frac{67 + 68 + 65 + 68 + 72 + 72 + 69 + 71}{8} = \frac{552}{8} = 69 \] Show more…
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The heights of mothers and daughters are given below: Height of mothers Height of daughters 64 63 66 62 65 59 66 62 66 62 68 64 64 61 65 63 63 60 65 62 Calculate the correlation coefficient for the heights of the mothers and daughters
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Use the sample data to construct a scatterplot. Use the first variable for the $x$ -axis. Based on the scatierplot, what do you conclude about a linear correlation? The table lists heights (in.) of fathers and the heights (in.) of their first sons (from Francis Galton). 8. Heights of Fathers and Sons The table lists heights (in.) of fathers and the heights (in.) of their first sons (from Francis Galton). $$\begin{array}{l|l|l|l|l|l|l|l|l|l|l} \hline \begin{array}{l} \text { Height of } \\ \text { father (in.) } \end{array} & 73.0 & 75.5 & 75.0 & 75.0 & 75.0 & 74.0 & 74.0 & 73.0 & 73.0 & 78.5 \\ \hline \begin{array}{l} \text { Height of first } \\ \text { son (in.) } \end{array} & 74.0 & 73.5 & 71.0 & 70.5 & 72.0 & 76.5 & 74.0 & 71.0 & 72.0 & 73.2 \\ \hline \end{array}$$
Exploring Data with Tables and Graphs
Scatterplots, Correlation, and Regression
Rank the correlations Consider each of the following relationships: the heights of fathers and the heights of their adult sons, the heights of husbands and the heights of their wives, and the heights of women at age 4 and their heights at age $18 .$ Rank the correlations between these pairs of variables from highest to lowest. Explain your reasoning.
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