QUESTION
A sample of 5 observations collected in a regression study on two variables, x(independent variable) and y(dependent variable). The sample resulted in the following data.
summation (x_i-xbar)2=15, summation (x_i-xbar)(y_i-ybar)=60, xbar=3, ybar=10
Calculate the y-intercept (b_0) of the estimated regression equation.
QUESTION
A sample of 13 observations collected in a regression study on two variables, x(independent variable) and y(dependent variable). The sample resulted in the following data.
summation (x_i-xbar)2=14, summation (x_i-xbar)(y_i-ybar)=72, xbar=3, ybar=10
Calculate the slope of the estimated regression equation.
10 points
QUESTION
A sample of 9 observations collected in a regression study on two variables, x(independent variable) and y(dependent variable). The sample resulted in the following data.
SSE=14, SSR=79
Calculate the coefficient of determination for the developed estimated regression equation.
Why did the regression equation go to the party alone? It wanted to find its y-intercept in peace!
To calculate the y-intercept (b_0) of the estimated regression equation, we need to use the following formula:
b_0 = ybar - b_1 * xbar
Given that xbar = 3, ybar = 10, and we are not given the value of b_1, we cannot determine the y-intercept without that information. So, unfortunately, the y-intercept remains a mystery!
To calculate the coefficient of determination (R^2), we need to know the total sum of squares (SST) as well. However, this information is not provided in the given data. Can you please provide the value of SST, or any additional information that can help calculate it?
To calculate the y-intercept (b0) of the estimated regression equation, we can use the formula:
b0 = ybar - b1 * xbar
where ybar is the mean of the dependent variable (y) and xbar is the mean of the independent variable (x), and b1 is the slope of the estimated regression equation.
First, let's calculate the slope (b1) using the given formula:
b1 = (sum((xi - xbar) * (yi - ybar))) / (sum((xi - xbar)^2))
For the given data, the values are:
summation (xi - xbar)^2 = 15
summation (xi - xbar)(yi - ybar) = 60
xbar = 3
ybar = 10
Substituting these values into the formula, we can calculate the slope (b1):
b1 = (60) / (15) = 4
Now, we can substitute the values into the formula to calculate the y-intercept (b0):
b0 = 10 - (4 * 3) = 10 - 12 = -2
Therefore, the y-intercept (b0) of the estimated regression equation is -2.
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To calculate the slope of the estimated regression equation, we can use the formula:
b1 = (sum((xi - xbar) * (yi - ybar))) / (sum((xi - xbar)^2))
where xbar is the mean of the independent variable (x) and ybar is the mean of the dependent variable (y).
For the given data, the values are:
summation (xi - xbar)^2 = 14
summation (xi - xbar)(yi - ybar) = 72
xbar = 3
ybar = 10
Substituting these values into the formula, we can calculate the slope (b1):
b1 = (72) / (14) = 5.14 (approx.)
Therefore, the slope of the estimated regression equation is approximately 5.14.
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To calculate the coefficient of determination for the developed estimated regression equation, we can use the formula:
R^2 = SSR / SST
where SSR is the sum of squares due to regression and SST is the total sum of squares.
For the given data, the values are:
SSE = 14
SSR = 79
To calculate SST, we need to use the formula:
SST = SSE + SSR
SST = 14 + 79 = 93
Now, we can calculate the coefficient of determination (R^2):
R^2 = SSR / SST = 79 / 93 = 0.849 (approx.)
Therefore, the coefficient of determination for the developed estimated regression equation is approximately 0.849.