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Anonymous asked in Science & MathematicsMathematics · 1 month ago

# T or F: The closer that data points fall to the regression line, the more closely two variables are related.?

I also need help with these stat questions, thanks!!

2) A correlation coefficient can ______ demonstrate cause.

A. always

B. never

C. mostly

D. intermittently

3) The regression equation measures ______.

A. how far the sample mean deviates from the population mean

B. how far each data point deviates from the line that most closely fits the data

C. how significant mean differences are between groups

D. how often scores regress from deviations in the data

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• 1) TRUE, in fact if all the data points fell on the trend line (aka, regression line) that would be a perfect fit.  y = f(x) with no errors or uncertainties.

2) B never.  The correlation coefficient never makes claims about cause and effect.  EX:  I can show a 1.00 coefficient for the sun rising and the rooster crowing in the morning, but that doesn't mean the rooster caused the sun to rise.

3) B.  We can actually draw by sight a pretty fair trend line by simply making the same number of data points fall above and below the line we draw...and by equal minimum distances from that line.

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• I'm no statistician, but I'm going to go with

1) T - If there was no relation between two variables, you would expect the scatter plot to be random. A best fit line would be tough to find in the first place. Now if they were very closely correlated, the data points would be very close to the best fit line.

2) D - Correlation does not always indicate causation. For example, if an increase in ice cream sales is closely correlated to the number of drowning deaths in the same area, that does not mean increased ice cream sales CAUSE people to drown. A possible explanation is that warmer temperatures are driving both ice cream sales AND volume of people at pools, increasing the risk of death by drowning. So the answer is not A, it is not B because sometimes the correlation can be a causal relationship, and it is not C because we cannot say a majority of cases are causal relationships.

3) B - pretty self explanatory

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