CORRECT WELL DETAILED ANSWERSLATEST

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CORRECT WELL DETAILED ANSWERS|LATEST

A researcher conducts an observational study and finds a correlation between managers' income and the number of college credits earned. The correlation coefficient was r=.85 with a regression equation of y=515x+12000. What can you say about the relationship between these variables?

a) There is an association between these variables

b) There is a causation between these variables.

c) There is no relationship between these variables.

d) There is not enough information to determine the relationship between the variables. -

ANSWER a) There is an association between these variables

Based on the correlation coefficient the researcher can conclude that there is an association between these variables.

If a trend appears in a large sample of data, the trend may not be replicated if the sample is broken up into smaller subsets. What is this effect known as?

a) Foster's Theorem

b) Bayes' Theorem

c) Simpson's Paradox

d) Consistency Construct - ANSWER c) Simpson's Paradox

Simpson's Paradox is a counterintuitive situation in which a trend in different groups of data disappears or reverses when the groups are combined.

What is the most appropriate definition of a scatterplot? 1 / 3

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a) A graph that uses dots to demonstrate relationships between two categorical variables.

b) A graph where lines are shown to represent positive or negative trends.

c) A graph where the explanatory and response variables are plotted as ordered pairs.

d) A graph where a positive causation is always represented with dots forming a straight line.

• ANSWER c) A graph where the explanatory and response variables are plotted as

ordered pairs.

A scatterplot is a graph that uses dots to represent ordered pairs on a coordinate plane to show the relationship between variables.

Using a line of best fit in slope-intercept form, y=mx+b, what must be true if there is a positive correlation?

• m must be >0.
• b must be >.

c) Both m and b must be>0.

d) Both m and b must have the same sign. - ANSWER m must be >0.

A positive correlation means the data points are following a linear pattern of going up and to the right. The line of best fit would also follow this and therefore have a positive slope.

A relationship between two or more variables is known as a(n) ________.

a) Causation

b) Association

c) Cause and effect

d) Correlation - ANSWER b) Association

An association is a pattern or relationship between two or more variables.

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When linear regression is used to show there is a linear association between two variables,

we know the relationship is:

a) A causation

b) A correlation

c) Neither A nor B

d) Both A and B - ANSWER b) A correlation

A linear association between two variables is a correlation. However, we are not able to conclude that the correlation is a causation. There may be reasons why this correlation is present that do not necessarily indicate that there is a causation. For example, a lurking variable may be causing the correlation, even without a cause-and-effect relationship between the two variables being studied.

Using the scatterplot Distance from City Center vs. Monthly Rent, how far can we expect an apartment to be from the city center if the monthly rent is $980? Round your answer to the nearest mile.

a) Around 54 miles

b) Around 55 miles

c) Around 56 miles

d) Around 57 miles - ANSWER b) Around 55 miles

Solving algebraically using the linear regression equation y=−0.0105x+10.381=- 0.0105+10.381 we can substitute 9.8 for y as the units on the y-axis are provided in $100s of dollars, 9.8=−0.0105x+10.3819.8

(9.80−10.381) / −0.0105=55.3333. Therefore, rounded to the nearest mile the answer is around 55 mile

What is (are) a potential problem(s) that can occur when attempting to use regression analysis?

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