Answer:
residual is the difference between what is plotted in your scatter plot at a specific point, and what the regression equation predicts "should be plotted" at this specific point. If the scatter plot and the regression equation "agree" on a y-value (no difference), the residual will be zero.
definition
Residual = Observed y-value - Predicted y-value
A residual is the difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line).
It is the vertical distance from the actual plotted point to the point on the regression line.
You can think of a residual as how far the data "fall" from the regression line
(sometimes referred to as "observed error").
Linear associations are the most popular statistical relationships since they are easy to read and interpret. We will spend the majority of our time working with linear relationships, and residuals can tell us when we have an appropriate linear model.
When you look at your scatter plot, and you are unsure if the shape (curve) you chose for your regression equation will create the best model, a residual plot will help you make a decision as to whether the model you chose will, or will not, be an appropriate linear model.
A residual plot is a scatter plot that shows the residuals on the vertical axis and the independent variable on the horizontal axis. The plot will help you to decide on whether a linear model is appropriate for your data.
Appropriate linear model: when plots are randomly placed, abov
Answer:
Step-by-step explanation:
To find the equation of the a line that passes through the two given points, we must first find the slope between the two points. We can do this by using the slope formula. The slope formula is:
where m is the slope and (x₁, y₁) and (x₂, y₂) are two points.
By plugging in (-2, -4) and (0, 5) for (x₁, y₁) and (x₂, y₂) respectively, we get:
So the slope is 9/2. Now we that we have found the slope, we can write an equation. Normally, when we are given two points, we would pick one of the points and plug it into the point-slope form and then solve for slope-intercept form. Here, notice that one of the points give, (0, 5), is the y-intercept. Knowing this, we can plug in 5 for the y-intercept into the slope-intercept form to get our equation. Remember, slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
Pugging in 9/2 for m and 5 for b we get:
which would be our equation.
I hope this helps. Happy studying.
Answer:
$72
Step-by-step explanation:
I = Prt
I = ($300)(0.04)(6)
I = $72
a) Jodi's car traveled 38 miles per gallon of gas. We know this because by dividng the amount of miles traveled by number of gallons Jodi has in her car we can find how many miles she travels per gallon of gas.
So our equation would be 456 / 12 = 38
b) The cost per gallon of gas was $3.74. We can find this answer by dividing how much she paid ($44.88) by how many gallons she bought (12).
So our equation would be 44.88 / 12 = 3.74
Answer:
The area of the shape after it has been enlarged by
scale factor 2 will be: 10 cm²
Step-by-step explanation:
The Area is basically a measure of how much space in square units there is inside an object.
As the shape is shown on the centimeter grid.
- The shape clearly occupies the space of 5-centimeter squares.
We also know that If the scale factor > 1, the image is enlarged.
As we know to determine the area of the shape after it has been enlarged by scale factor 2, all we need to do is to multiply the area of the original shape by 2.
The area of original shape = 5 cm²
The area of the shape after the dilation by a scale factor 2 = 5 × 2 = 10 cm²
Thus, the area of the shape after it has been enlarged by
scale factor 2 will be: 10 cm²