Answer:
1) Estimated slope = b₁ = 0.215
2) Estimated y-intercept = b₀ = -4.185
3) Not all the points predicted fall on the same straight line, but the model gives a close to ideal estimate of the line of best fit.
4) The estimated value of y when x=46 is 5.705
5) The value of the dependent variable y^ at x=0 is -4.185
6) The coefficient of determination = 0.951
Step-by-step explanation:
To solve this, we apply regression analysis
y = b₀ + b₁x
Price in Dollars | 23 | 34 | 40 | 46 | 47
Number of Bids | 1 | 3 | 4 | 5 | 7
For this question, we want to predict the number of bids (dependent variable, y), given the list price of the item (independent variable, x)
So, running the analysis on a spreadsheet application, like excel, the table of parameters is obtained and presented in the first attached image to this solution.
Σxᵢ = sum of all the independent variables (sum of all the list prices)
Σyᵢ = sum of all the dependent variables (sum of all the number of bids in the table)
Σxᵢyᵢ = sum of the product of each dependent variable and its corresponding independent variable
Σxᵢ² = sum of the square of each independent variable (list prices)
Σyᵢ² = sum of the square of each dependent variable (number of bids)
n = number of variables = 5
The scatter plot and the line of best fit is presented in the second attached image to this solution
Then the regression analysis is then done
Slope; m = b₁ = [n×Σxᵢyᵢ - (Σxᵢ)×(Σyᵢ)] / [nΣxᵢ² - (∑xi)²]
Intercept b: b₀ = [Σyᵢ - m×(Σxᵢ)] / n
Mean of x = (Σxᵢ)/n
Mean of y = (Σyᵢ) / n
Sample correlation coefficient r: r =
[n*Σxᵢyᵢ - (Σxᵢ)(Σyᵢ)] ÷ {√([n*Σxᵢ² - (Σxᵢ)²][n*Σyᵢ² - (Σyᵢ)²])}
And -1 ≤ r ≤ +1
All of these formulas are properly presented in the third attached image to this answer
The table of results; mean of x, mean of y, intercept, slope, regression equation and sample coefficient is presented in the fourth attached image to this answer.
Hence, the regression equation is
y = -4.185 + 0.215x
y = b₀ + b₁x
Intercept = b₀ = -4.185
Slope = b₁ = 0.215
And the regression coefficient = 0.951 (Which is very close to 1 and indicates statistic significance)
Hence, we can use this answer obtained to answer the questions attached
1) Find the estimated slope.
Estimated slope = b₁ = 0.215
2) Find the estimated y-intercept.
Estimated y-intercept = b₀ = -4.185
3) Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.
Taking a few of sample data
x = 23 when y = 1
y = -4.185 + 0.215x
y = -4.185 + 0.215 (23) = 0.76 ≈ 1
x = 34, y = 3
y = -4.185 + 0.215 (34) = 3.125 ≈ 3
Hence, it is evident that not all the points predicted fall on the same straight line, but the model gives a close to ideal estimate of the line of best fit.
4) Find the estimated value of y when x=46.
The linear model is
y = -4.185 + 0.215x
when x = 46
y = -4.185 + 0.215(46) = 5.705
5) Determine the value of the dependent variable y^ at x=0.
y = -4.185 + 0.215x
when x = 0
y = -4.185 + 0.215(0) = -4.185
6) Find the value of the coefficient of determination.
The coefficient of determination = regression coefficient = 0.951 (as calculated above)
Hope this Helps!!!
For this case we have the following data:
Area of the rectangle,
Relationship of the sides 5: 3
By definition, the area of a rectangle is given by:
Where
If the sides have a 5: 3 ratio, it means:
Substituting in the formula of the area, we have:
Clearing b:
units
Substituting and clearing:
units
So, the sides are:
units
units
Answer:
units
units
Answer:
D. inches.
Step-by-step explanation:
We have been given that the circle with center O has a minor arc BSA with a length of inches. The central angle is 40°.
To find the circumference of circle we will use formula:
, where
= measure of 360 degrees in radians and
= circumference of circle.
Let us convert measure of central angle into radians.
Upon substituting our given value in the formula we will get,
Cross multiplying we will get,
Hence, the radius of our circle is 27/4 inches.
Since the circumference of circle is . Upon substituting
we will get,
Therefore, circumference of our given circle will be inches and option D is the correct choice.