Suppose we fit the least-squares regression line to a set or data. The plot of i

Question

Suppose we fit the least-squares regression line to a set or data. The plot of is given below. a straight line is not a good summary for the data. the correlation must be 0 the correlation must be positive. outliers must be present. The correlation between the height and weight of children aged 6 to9 is found to be about r = 0.8. Suppose we use the height x of a child to predict the weight y of the child. We conclude that the least-squares regression line of y on x would have a slope of 0.8 about of the time, age will accurately predict weight. height is generally 60% of a child's weight. The fraction of variation in weight explained by the least-squares regression line of weight on height is 0.64.

Explanation / Answer

Question 21: Clearly from the plot we see that it is more like a quadratic second degree polynomial which would be a good approximation for the relationship between the 2 variables and not a straight line. Therefore a) is the correct answer here.

Question 22:

The coefficient of determination is the square of the correlation coefficient. Therefore the coefficient of determination would be = 0.82 = 0.64.

Therefore the fraction of variation explained by the least square regression line of weight on height would be 0.64 ( that is the definition of R2 that is the coefficient of deterimnation. Therefore d) is the correct answer here.

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