Which is the explanatory\' variable? Which is the response? c. Without software

Question

Which is the explanatory' variable? Which is the response? c. Without software the correlation coefficient is tedious to calculate and lends itself to many arithmetic mistakes. A student tries to calculate the correlation coefficient a few times by hand but each time they get a different answer. Ugh! Fortunately they know that one of their answers is three answers for the correlation coefficient they calculated are: - 0.61, 0.84 and 0.09. Which of these the correct correlation? Describe why the value you chose makes sense to be the correct correlation the others cannot be correct. d. Using the software output to the right or your T1-84. Find the equation of the least-squares line for estimating temperature given cricket chirps per second. In the context of the problem what does the intercept represent? What does the slope represent? e. Using the least-squares regression equation estimate temperature for when crickets are chirping at a rate of 16 chirps per second. Based on the data does this seem like a reasonable prediction? Why?

Explanation / Answer

Part (a)

Without the actual data, it is not possible to guess which of the 3 values is the correct one. Given that ‘they know that one of their answers is correct’, a crude logic would pick – 0.61 as the correct correlation since there is only one negative out of 3.

[If actual data were available, without actually calculating, the correct one out of 3 can be guessed fairly well. If x and y are moving in opposite directions, answer is clearly – 0.61. If both x and y move in the same direction, – 0.61 is ruled out. Further, taking 2 or 3 pairs of (xi, yi) if the ratio of yi to xi is fairly close to each other, it is an indication that x and y are strongly related and hence one could guess the correct answer is 0.86]   

Part (b)

In the regression model, y = + x, if a and b are the least square estimates of and , then

a represents the ‘intercept’ and b represents the coefficient or slope. So, if y = temperature and

x = chirps per second, then the regression equation is y = 25.2 + 3.3x.

In this equation, the intercept 25.2 should be interpreted as the temperature when chirps per second is zero and the slope 3.3 represents the expected increase/decrease in temperature when chirps per second increase/decrease by 1 unit. ANSWER

Part (c)

Substituting x = 16, the estimated temperature is 25.2 + (3.3x16) = 78 ANSWER

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