Question

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below.
Performance 59 63 65 69 58 77 76 69 70 64
Attitude 72 67 78 82 75 87 92 83 87 78
Be sure to use the appropriate explanatory and the appropriate response variable.
a. y = 92.3 - 0.669x
b. y = 100.3 - 0.453x
c. y = 11.7 + 1.02x
d. y = 2.81 + 1.35x
e. y = -47.3 + 2.02x

Answer 1

Answer:

The answer is "choice c".

Step-by-step explanation:

Below, we shall find the line equation, dissociation for both the management's behavior and achievement.

Here, attitudes are the response variable while performance seems to be the predictor as attitude is achievement dependant.

If Y indicates the attitude while X relates to workers' performance.

Let's describe the data like:

$y=a+bx+e$

Now we get the estimates of e via the least quadratic method, – i.e., by reducing the number of segments.

$S=\sum e_{i}^{2}=\sum {(y_{i}-a-bx_{i})^{2}}$

minimize S to obtain the estimates of a and b as:

$\hat{b}=\frac{\sum{(y_{i}-\bar{y})(x_{i}-\bar{x})}}{\sum{(x_{i}-\bar{x})^{2}}}\\\\\hat{a}=\bar{y}-\hat{b}\bar{x}$

So,

$a=11.7b=1.02$

Equation:

$Y=11.7+1.02x$