For a set of data, x is the explanatory variable. Its mean is 8.2, and its standard deviation is 1.92. For the same set of data, y is the response variable. Its mean is 13.8, and its standard deviation is 3.03. The correlation was found to be 0.223. Select the correct slope and y-intercept for the least-squares line.
a. Slope = -0.35
y-intercept = -10.9
b. Slope = -0.35
y-intercept = 10.9
c. Slope = 0.35
y-intercept = -10.9
d. Slope = 0.35
y-intercept = 10.9

Slope & Intercept are : D) 0.35 , 10.9

Regression is the relationship between explanatory (independent) & dependent variable, which are x & y respectively.

The regression equation y = a + bx + c has intercept & slope a & b respectively , formula for finding them are as follows :

b = r ( σy / σ x )

0.223 ( 3.03 / 1.92 )

= 0.223 (1.578125)

= 0.3519

a = Y' - bX'

a = 13.8 - 0.3519 ( 8.2 )

= 13.8 - 2.8558

= 10.91

Regression Equation : y = 10.9 + 0.35x

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d. Slope = 0.35

y-intercept = 10.9

Step-by-step explanation:

The computation is shown below:

Data given in the question

Mean = 8.2

The standard deviation  of x = = 1.92

Mean = 13.8

The standard deviation  of y = = 3.03

The correlation = r = 0.223

Based on the above information,

As we know that

The slope is

= 0.3519

Now the y-intercept is

= 13.8  - (0.351922) 8.2

= 13.8 - 2.88579

= 10.91

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175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175