(02.04 HC) A random sample of online makeup tutorial videos and sales of makeup was measured, and the computer output for regression was obtained:

Coefficients Standard Error t Stat P-value

Intercept −7.567857143 0.426240686 −17.7549 1.04E-05

Makeup Tutorial Videos 0.917857143 0.028166777 32.58652 5.11E-07

R-sq. = 99.53% R-sq. (adj) = 99.44%

Part A: Use the computer output to determine the LSRL. Identify all the variables used in the equation. (3 points)

Part B: What proportion of the variation in makeup sales is explained by its linear relationship to makeup tutorial videos? Explain. (4 points)

Part C: Determine if increased makeup sales were caused by online makeup tutorial videos. Explain your reasoning. (3 points)

Explained below.

Step-by-step explanation:

A.

The least square regression line is:

Here,

y = estimated sales of makeup

x = number of online makeup tutorial videos

a = -7.568 = intercept

b = 0.918 = slope of the regression line

B.

The coefficient of determination R² specifies the percentage of the variance in the dependent-variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).

So, the proportion of the variation in makeup sales that can be explained by its linear relationship to makeup tutorial videos is 99.53%.

C.

Consider the LSRL.

The slope of the regression line is positive, i.e. there is a positive relationship between the makeup sales and the online makeup tutorial videos.

So, with one unit increase in the online makeup tutorial videos the makeup sales goes up by 0.918 units.

Thus, it can be said that the increased makeup sales were caused by online makeup tutorial videos.

the area of the rectangle is 35units^2.

step-by-step explanation:

graph it and find the distance.

it is a 5*7 rectangle.

therefore the area is 35units^2.

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²