A researcher obtained the average SAT scores of all students in each of the 50 s

Question

A researcher obtained the average SAT scores of all students in each of the 50 states, and the average teacher salaries in each of the 50 states. She found a negative correlation between these variables. The researcher concluded that a lurking variable must be present. By lurking variable she means A. a variable that is not among the variables studied but which affects the response variable. B. the true cause of a response. C. any variable that produces a large residual. D. the true variable, which is explained by the explanatory variable. Curiously, during months when sales of beer are above average, sales of ice cream also tend to be above average; during months when sales of beer are below average, sales of ice cream also tend to be below average. Which of the following can we conclude from these facts? A. The correlation between "beer sales" and "ice cream sales" is negative. B. For a lot of people, drinking beer causes a desire for ice cream, or vice versa. C. A scatterplot of monthly ice cream sales vs. monthly beer sales would show that a straight line describes the pattern in the plot, but it would have to be a horizontal line. D. None of the above. Which of the following statements is true? A. The correlation coefficient equals the proportion of times two variables lie on a straight line. B. The correlation coefficient will be +1.0 only if all the data lie on a perfectly curved line. C. The correlation coefficient measures the fraction of outliers that appear in a scatterplot. D. The correlation coefficient is a unitless number and must always lie between -1.0 and +1.0, inclusive. A researcher states that bone density in women is negatively associated with age. This means A. above average values of age tend to accompany below average values of bone density. B. above average values of age tend to accompany above average values of bone density. C. below average values of age tend to accompany below average values of bone density. D. older women aren't any more likely than younger

Explanation / Answer

5. A lurking variable is a variable that is not included as an explanatory or response variable in the analysis but can affect the interpretation of relationships between variables. Alurking variable can falsely identify a strong relationship between variables or it can hide the true relationship. Hence the answer is

Option (A) : A variable that is not among the variables studied but whuch affects the response variable

6. This means that there is a positive corrleation between the average sales of beer & average sale of ice cream/ Hence the answer is Option (D). None of the above.

7. In statistics, the correlation coefficient r measures the strength and direction of a linear relationship between two variables on a scatterplot. Hence the answer is Option(D).

It is a unitless number and must always lie between -1 and +1, inclusive

8. Two variables are said to be negatively correlated, if increase in one leads to decraese in the another and vice versa. Hence the answer is Option(A)

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