Q15: According to the following graphic, X and Y have 130 120 110 100 80 70 1400

Question

Q15: According to the following graphic, X and Y have 130 120 110 100 80 70 1400 1600 800 2000 2200 2400 A. virtually no correlation B. strong negative correlation C. strong positive correlation D. moderate negative correlation Q16: For a regression model y 30-2x, the coefficient of determination was determined as equal to 0.81. The coefficient of correlation is A.-0.9 B. 0.81 C. 0.6561 D. 0.9 Q17: In fitting a least square line to n 10 data points, the following quantities were computed: SSxx 32, X-3, SSyy 26, P-4, SSxy 28, then the coefficient of determination is A. 0.9707 B. 0.9901 C. 0.9423 D. 0.98

Explanation / Answer

Answer 15. (Option B)

As the value of x is increasing, the value of y is increasing but not very linearly as the points are scattered in space. Also ,as r is close to 1 ( can be related to the scattering of points), it tells us that the linear relationship is very strong, but not perfect.

Answer 16. (Option A.)

We know that,

[coefficient of correlation (r)]2 = coefficient of determination

Here, d=0.81

Therefore,

r2 = 0.81

r = -0.9 and +0.9.

Now, we have

y = 30 - 2x

which means that as value of x is increasing, value of y is decreasing which depicts a negative coorelation.

Hence, r = -0.9.

Answer 17. (Option A).

We can use the formula for determination of coefficient of correlation (r).

We have,

R = SSxy / (SSxx*SSyy)0.5 = 28 / 28.8444 = 0.9707.

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