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1. Find the least squares regression line for the dataset in the table
x|y
3|1
4|5
8|11
10|21
a. y=2.55x-6.435
b. y=2.55x+6.435****
c. y=1.477x+1.477
d. y=1.698x
2. y=2,060-0.186x is the line of regression of a table of values comparing full-front crash repair costs to full rear crash repair costs for a certain model sedan. Use the equation to predict the full-rear repair cost from a full-front repair cost of $4,594.
a. $13,624
b. $1,206****
c. $22,639
b 1,206
I just took the quiz. It's {B. $1,206}
b. $1,206
1. To find the least squares regression line, we need to calculate the slope and y-intercept using the given dataset.
Step 1: Find the mean of x and y values.
Sum of x values = 3 + 4 + 8 + 10 = 25
Sum of y values = 1 + 5 + 11 + 21 = 38
Mean of x values = 25 / 4 = 6.25
Mean of y values = 38 / 4 = 9.5
Step 2: Calculate the slope.
Slope (m) = Σ((xi - x_mean) * (yi - y_mean)) / Σ((xi - x_mean)^2)
= ((3 - 6.25) * (1 - 9.5) + (4 - 6.25) * (5 - 9.5) + (8 - 6.25) * (11 - 9.5) + (10 - 6.25) * (21 - 9.5)) / ((3 - 6.25)^2 + (4 - 6.25)^2 + (8 - 6.25)^2 + (10 - 6.25)^2)
= (-3.25 * -8.5 + -2.25 * -4.5 + 1.75 * 1.5 + 3.75 * 11.5) / (4.5 + 2.5 + 2.5 + 3.5)
= (27.625 + 10.125 + 2.625 + 43.125) / 13.0
= 83.5 / 13.0
= 6.42
Step 3: Calculate the y-intercept.
y-intercept (b) = y_mean - (m * x_mean)
= 9.5 - (6.42 * 6.25)
= 9.5 - 40.125
= -30.625
Therefore, the least squares regression line for the given dataset is y = 6.42x - 30.625.
Answer: None of the provided options is correct. The correct answer is y = 6.42x - 30.625.
2. To predict the full-rear repair cost from a full-front repair cost of $4,594 using the given equation y = 2,060 - 0.186x, substitute x = 4,594 into the equation.
y = 2,060 - 0.186(4,594)
= 2,060 - 853.284
= 1,206.716
Therefore, the predicted full-rear repair cost from a full-front repair cost of $4,594 is $1,206.716, which can be rounded to $1,206.
Answer: b. $1,206
1. To find the least squares regression line for a dataset, you need to calculate the slope (m) and the y-intercept (b) using the following formulas:
mean_x = (sum of all x-values) / (total number of data points)
mean_y = (sum of all y-values) / (total number of data points)
slope (m) = Σ((x - mean_x) * (y - mean_y)) / Σ((x - mean_x)^2)
y-intercept (b) = mean_y - (slope * mean_x)
Let's calculate the least squares regression line for the dataset:
x|y
3|1
4|5
8|11
10|21
1. Calculate the mean of x and y:
mean_x = (3 + 4 + 8 + 10) / 4 = 25 / 4 = 6.25
mean_y = (1 + 5 + 11 + 21) / 4 = 38 / 4 = 9.5
2. Calculate the slope (m):
m = [(3 - 6.25) * (1 - 9.5) + (4 - 6.25) * (5 - 9.5) + (8 - 6.25) * (11 - 9.5) + (10 - 6.25) * (21 - 9.5)]
/ [(3 - 6.25)^2 + (4 - 6.25)^2 + (8 - 6.25)^2 + (10 - 6.25)^2]
= (-3.25 * -8.5 + (-2.25) * (-4.5) + 1.75 * 1.5 + 3.75 * 11.5) / (9 / 16 + 25 / 16 + 9 / 16 + 25 / 16)
= (27.625 - 10.125 + 2.625 + 43.125) / (68 / 16)
= 63.25 / 4.25
= 14.88235294117647
3. Calculate the y-intercept (b):
b = mean_y - (slope * mean_x)
= 9.5 - (14.88235294117647 * 6.25)
= 9.5 - 92.89
= -83.39
Therefore, the least squares regression line for the dataset is y = 14.88235294117647x - 83.39.
Now, let's check the answer choices:
a. y=2.55x-6.435
b. y=2.55x+6.435
c. y=1.477x+1.477
d. y=1.698x
Based on our calculations, the answer is b. y=2.55x+6.435, so the correct answer is b.
2. To use the equation y = 2,060 - 0.186x to predict the full-rear repair cost from a full-front repair cost of $4,594, substitute x = 4,594 into the equation:
y = 2,060 - 0.186 * 4,594
= 2,060 - 852.484
= 1,207.516
The predicted full-rear repair cost is approximately $1,207.516.
Now, let's check the answer choices:
a. $13,624
b. $1,206
c. $22,639
Based on our calculation, the answer is b. $1,206, so the correct answer is b.