Chapter 4: Problem 2
Explain what is meant by a lurking variable. Provide an example.
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These are the key concepts you need to understand to accurately answer the question.
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Chapter 4: Problem 2
Explain what is meant by a lurking variable. Provide an example.
These are the key concepts you need to understand to accurately answer the question.
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Consider the following set of data: $$\begin{array}{lllllllll} x & 2.2 & 3.7 & 3.9 & 4.1 & 2.6 & 4.1 & 2.9 & 4.7 \\ \hline y & 3.9 & 4.0 & 1.4 & 2.8 & 1.5 & 3.3 & 3.6 & 4.9 \end{array}$$ (a) Draw a scatter diagram of the data and compute the linear correlation coefficient. (b) Draw a scatter diagram of the data and compute the linear correlation coefficient with the additional data point \((10.4,9.3) .\) Comment on the effect the additional data point has on the linear correlation coefficient. Explain why correlations should always be reported with scatter diagrams.
What does it mean to say that the linear correlation coefficient between two variables equals \(1 ?\) What would the scatter diagram look like?
For each of the following statements, explain whether you think the variables will have positive correlation, negative correlation, or no correlation. Support your opinion. (a) Number of cigarettes smoked by a pregnant woman each week and birth weight of her baby (b) Annual salary and years of education (c) Number of doctors on staff at a hospital and number of administrators on staff. (d) Head circumference and IQ (e) Number of moviegoers and movie ticket price.
(a) Draw a scatter diagram treating \(x\) as the explanatory variable and \(y\) as the response variable. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Determine the least-squares regression line. (e) Graph the least-squares regression line on the scatter diagram. (f) Compute the sum of the squared residuals for the line found in part (b). (g) Compute the sum of the squared residuals for the least-squares regression line found in part (d). (h) Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d). $$\begin{array}{c|ccccc}x & -2 & -1 & 0 & 1 & 2 \\\\\hline y & -4 & 0 & 1 & 4 & 5\end{array}$$
What does it mean to say that two variables are positively associated?
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