The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
Age 47 49 51 58 63
Bone Density 360 353 336 333 332
Step 1 of 6:Find the estimated slope. Round your answer to three decimal places.
Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.
Step 3 of 6: Find the estimated value of y when x=47 Round your answer to three decimal places.
Step 4 of 6: According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable yˆ is given by? (b0, b1, x, y)
Step 5 of 6: Find the error prediction when x=47. Round your answer to three decimal places.
Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Step 1: To find the estimated slope (b1), we first need to calculate the means of both x (age) and y (bone density). After that, we'll find the product of the deviations of each point from their respective means, sum them up, and divide by the sum of the squared deviations of x values from their mean. The estimated slope is -1.342.

Step 2: To find the estimated y-intercept (b0), use the formula b0 = mean(y) - b1 * mean(x). The estimated y-intercept is 424.995.
Step 3: To find the estimated value of y when x=47, use the regression line equation: yˆ = b0 + b1 * x. When x=47, yˆ = 424.995 - 1.342 * 47 ≈ 362.851.
Step 4: If the value of the independent variable (x) is increased by one unit, the change in the dependent variable (yˆ) is given by the slope, b1. In this case, it is -1.342.
Step 5: To find the error prediction when x=47, subtract the actual bone density from the predicted bone density: error = actual - predicted = 360 - 362.851 ≈ -2.851.
Step 6: To find the coefficient of determination (R²), square the correlation coefficient (r). First, find r using the sum of products of deviations of x and y values divided by the product of the square roots of the sum of squared deviations of x and y values. In this case, r ≈ -0.981. Thus, R² ≈ 0.962.

Learn more about density here

https://brainly.com/question/1354972

#SPJ11

1. The Clock
[tex] \sqrt{81} [/tex]
​

I need help ASAP !!
Find the length of a

Which expression is equivalent 10x+10
A.2x+5x+4x+5+5
B.2x+8x+1+3+6
C.5x+5x+2+4+4+1
D.2x+9x+5+5
(7th grade) Combing like terms.

2x3(5-4)/6.2
Algebra

Here is a polygon. Use the scale factor of 1/2 determine the new side length for A *

maths homework please help me

What’s 20 times 69?????

∆ has the coordinates (3, 1), (5, 2), (4, 3). ∆´´´ has coordinates (-1, 2), (1, 3) and (0, 4). Which choice describes the translation of ∆ to ∆´´? A +4 units in the direction of x and -1 units in the direction of y B -4 units in the direction of x and +1 units in the direction of y C +4 units in the direction of x and +1 units in the direction of y D -4 units in the direction of x and -1 units in the direction of y

‼️ PLEASEEE HELPP ‼️

como simplificar 9/3​

1. Three different scout troops have 12, 24, and 18 members. These troops must march together in a parade in
the same number of columns. What is the greatest possible number of scouts in each column?
9 scouts
b. 6 scouts
c. 8 scouts
d. 4 scouts

what is the percent of change from 85 to 64

el area de un rectangulo es 84 cm cuadrados si la base mide 9 cm cuanto mide la altura y cual es su perimetro?​

What expression is equivalent to 1/3 x -1/5

HELP QUICK. By combining three equations, it can be shown that a2+b2=c2. One of the equations is c=e+f. Which of the following could be the other two equations?

Solve the equation y – 5x = –7 for y.
A. y = 5x – 7
B. y = –5x – 7
C. y = 5x + 7
D. y = –5x + 7

If the sum of the interior angles of a polygon is 29160, how many sides does it have?

40 POINTS!
3. Suppose a point at (2,3) is translated to (7,-1). What rule describes this translation?
O A. (x, y) + (x + 5, y - 4)
O B.(z,y) → (2 – 5,y + 4)
O c.(x, y) = (x + 9,y - 2)
O D. (x, y) → (2 – 9,y + 2)

Which phrase describes the algebraic expression 5+w
A: the product of 5 and w
B: the quotſent of 5 and w
C: w more than 5
D: 5 less than w

NEED HELP AND RIGHT ANSWER DONT RUSH! REWARD BRAINLIEST

The dimensions for a rectangular prism are x + 3 for the length, x + 2 for the width, and x for the height. What is the volume of the prism? Enter your answer as a polynomial in standard form.

Is 5 a solution to 3x=35

Leah puts together gift bags of toys to sell at the flee market. She places exactly 6 toys in each bag. She only sells full bags of toys Leah has 280 toy cars. She can fill 46 toy cars Part B Leah has enough toy trucks to fill 25 gift bags. How many toy cars and toy trucks were put in gift bags to sell at the flee market

I don't understand this? help me! Linear functions 9th-grade math

What is the value of y when the value of x is 1

Please help, will mark brainliest, do not do for points or I will report, explanation please or no brainliest
Multiply.
2y - 1
2y + 1
4y^2 + 1

k + 11 = -3k- 25 + 2k

4x - (-6) what’s the answer

Kailey is thinking of two numbers. The larger number is equal to twice the smaller increased by 12. Two times the smaller number plus three times the larger is equal to 100. Let x = smaller number and y = larger number. What is the first equation in the system? Do not put spaces in your answer.

Select all ordered pairs that satisfy the function y =
= 8x + 3
A.
(0,3)
B.
(-1, 43)
C.
(0, -45)
D.
(5, 43)