Question

A set of n = 8 ordered pairs has the following sums. x = 111 x2 = 1,869 y = 618 y2 = 49,374 xy = 7,860

(a) Find the line of best fit. (Round your answers to one decimal place.) ŷ = x +

(b) Predict the value of y when x = 5. (Round your answer to one decimal place.) y =

(c) Predict the value of x when y = 60. (Round your answer to one decimal place.) x =

(d) Find the coefficient of linear correlation. (Round your answer to three decimal places.)

(e) Are the predictions in parts (b) and (c) reliable? Why or why not?

No, they are not reliable since the slope is negative.

No, they are not reliable since the correlation coefficient is close to −1.

Yes, they are reliable since the correlation coefficient is close to −1.

Yes, they are reliable since the slope is negative.

Yes, they are reliable since the correlation coefficient is close to 1.

Answer 1

We have the following

Get these sum of squares

Let the regression line being estimated be

(a) Find the line of best fit. (Round your answers to one decimal place.)

The estimated value of the slope is

The estimated value of the intercept is

ans: the line of best fit is

(b) Predict the value of y when x = 5. (Round your answer to one decimal place.)

Using x=5 in the equation, we get

ans: y=96.4

Note: if we use unrounded values for the estimated coefficients, then y=96.5

(c) Predict the value of x when y = 60. (Round your answer to one decimal place.)

Using y=60, we get

ans: x=21.5

Note: x=21.8 if we use the unrounded values for the coefficients

(d) Find the coefficient of linear correlation. (Round your answer to three decimal places.)

The coefficient of linear correlation is

ans: the coefficient of linear correlation is -0.975

(e) Are the predictions in parts (b) and (c) reliable? Why or why not?

A correlation coefficient of 1 or -1 indicates a perfect linear relationship between the 2 variables. Here, the correlation coefficient is close to -1, indicating a very high degree of linear relationship between x,y

ans: Yes, they are reliable since the correlation coefficient is close to −1.