Numerous scientific studies indicate that calcium is an essential mineral for th
ID: 3073848 • Letter: N
Question
Numerous scientific studies indicate that calcium is an essential mineral for the formation and maintenance of strong, healthy bones. An inadequate supply of calcium in the diet is broadly believed to contribute to weak, porous bones, increasing the risk of a hip fracture, especially in the elderly. Calcium can be obtained from several sources, including soybeans, many leafy green vegetables, and dairy products. 600 400 The scatterplot and superimposed regression line depict relationship between the annual incidence rate of hip fracture and the annual rate of dairy consumption for a sample of forty nations. 200 The regression analysis reveals a highly significant positive linear correlation between the variables. The sample linear correlation coefficient, r, is.852. Note that this positive relationship is opposite from what you would expect. 100 200 300 Dairy consumption (kg per capita) Select the plausible explanation of the relationship between the incidence rate of hip fracture and the rate of dairy consumption depicted in the scatterplot. O when the relationship between two variables is nonlinear, the actual relationship between the variables i typically the opposite as that indicated by the sample linear correlatio O The linear correlation coefficient of 0.852 is outside the valid range, so this indicates that there is no correlation between the incidence rate of hip fracture and the rate of dairy consumption. The sample size of 40 world nations is not large enough to establish any relationship. The linear correlation and regression analysis are invalid. the regression line does not have a meaningful y-intercept, it is inappropriate to interpret the sample linear correlation coefficient to indicate a positive relationship. is at least one lurking variable that correlates with both dairy consumption and hip fractures.Explanation / Answer
If the relationship between two variables is non linear then the data would show a curve like pattern however it does not affect the correlation coefficient in an opposite way. The value of the correlation coefficient lies between -1 to +1. Our value of 0.852 lies within this range so option 2 is incorrect. A sample size of 40 is sufficient to establish a relationship between the variables so option 3 is also incorrect. There is no evidence from the scatterplot to conclude that the line does not have a meaningful y- intercept. So option 4 is also incorrect.
Option 5 is correct. We can clearly see that there are a lot of lurking variables in the scatterplot that correlates with both dairy consumption and hip fractures.
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