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

rx and sx

step-by-step explanation:

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.