Variable year is categorical and therefore the

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variable, year, is categorical and therefore the article cannot state there is a correlation between the two variables. c) i) The scatterplot shows a negative linear relationship between X and Y. The correlation is strong at -0.967. There are no outliers. ii) The scatterplot shows a negative linear relationship between X and Y. The correlation is strong at -0.998. There are no outliers. iii) The scatterplot shows a positive linear relationship between X and Y. The correlation is +0.656. iv) By combining all of the observations, the linear relationship between the variables has reversed and the correlation is now weaker with a positive association. This is an example of Simpson’s Paradox. d) i) There is a negative linear relationship between Total Mortgages and Interest Rate . The correlation appears to be strong, with lots of clustering around the line and no outliers.
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ii) If we standardized both variables, the correlation coefficient would stay the same because standardizing doesn’t affect the strength of the association. iii) If we measured Total Mortgages in thousands of dollars instead of millions of dollars, the correlation coefficient would not change. iv) If the data point of 11% interest rates and $250 million mortgages were included, the correlation coefficient would decrease (but it would stay negative). v) This scatterplot provides fairly strong proof that if mortgage rates are lowered, people will take out more mortgages. However, again, correlation does not mean correlation and there could be lurking third variables affecting the data. We cannot be sure of this relationship based on these
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