Answer:
Step-by-step explanation:
Hello!
Given the independent variable X and the dependent variable Y (see data in attachment)
The regression equation is
^Y= b₀ + bX
Where
b₀= estimation of the y-intercept
b= estimation of the slope
The formulas to manually calculate both estimations are:
n=7
∑X= 42
∑X²= 292
∑Y= 49
∑Y²= 403
∑XY= 249
^Y= 13.75 - 1.13X
Using the raw data you can calculate the coefficient of determination as:
![R^2= \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]}](https://tex.z-dn.net/?f=R%5E2%3D%20%5Cfrac%7Bb%5E2%5BsumX%5E2-%5Cfrac%7B%28sumX%29%5E2%7D%7Bn%7D%20%5D%7D%7B%5BsumY%5E2-%5Cfrac%7B%28sumY%29%5E2%7D%7Bn%7D%20%5D%7D)
![R^2= \frac{(-1.13)^2[292-\frac{(42)^2}{7} ]}{[403-\frac{(49)^2}{7} ]}= 0.84](https://tex.z-dn.net/?f=R%5E2%3D%20%5Cfrac%7B%28-1.13%29%5E2%5B292-%5Cfrac%7B%2842%29%5E2%7D%7B7%7D%20%5D%7D%7B%5B403-%5Cfrac%7B%2849%29%5E2%7D%7B7%7D%20%5D%7D%3D%200.84)
This means that 84% of the variability of the dependent variable Y is explained by the response variable X under the model ^Y= 13.75 - 1.13X
I hope this helps!
Answer:
the slope is: -1/2
y-intercept: (0,-f)
hopefully that makes sense
Answer:
Width of the rectangle = 15 inches
Length of the rectangle = 25 inches
Step-by-step explanation:
Let the width of the rectangle = k inches
So, the length of the rectangle = (2k -5) inches
Perimeter = 80 in
Perimeter of a rectangle = 2 (Length + Width)
⇒ 80 = 2(k + (2k -5)
or 80 = 6k - 10
⇒ 6k = 80 + 10 = 90
or k = 90 / 6
⇒ k = 15
So the width of the rectangle = k = 15 inches
And the length of the rectangle = 2k -5 = 2 x 25 - 5 = 25 inches
Answer:
54
Step-by-step explanation:
Subtract 7 from 331 and then divide the answer by 6
331 - 7 = 324
324 ÷ 6 = 54
There are 54 students on each bus
Answer:
.
Step-by-step explanation:
