How many parallel lines does a regular pentagon have?
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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!!!
If you mean , then the answer is 3.
In fact, rational exponents work like this:
So, in your case,
because
The total of 42 swimmers are competing
Step-by-step explanation:
The given is:
- The ratio of runners to swimmers was 3 : 2
- When 28 runners dropped out of the competition, the ratio became 5 : 6
We need to find how many total swimmers are competing
∵ The ratio of runners to swimmers was 3 : 2
- Multiply each term of the ratio by x
∴ There are 3x runners and 2x swimmers
∵ 28 runners dropped out of the competition
∴ The number of runners who complete = 3x - 28
∵ The ratio became 5 : 6
- Equate the ratio between the new number of runners and the
number of swimmers by 5 : 6
∵ The new number of runners = 3x - 28
∵ The number of swimmers = 2x
∴
- By using cross multiplication
∴ 6(3x - 28) = 5(2x)
- Simplify both sides
∴ 18x - 168 = 10x
- Add 168 to both sides
∴ 18x = 10x + 168
- Subtract 10x from both sides
∴ 8x = 168
- Divide both sides by 8
∴ x = 21
∵ The number of swimmers is 2x
∵ x = 21
∴ The number of swimmers = 2(21) = 42
The total of 42 swimmers are competing
Learn more:
You can learn more about the ratio in brainly.com/question/2707032
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