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

i think it might be a but you might want a second opinion

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get