Questions: A new mine opened and the number of dump truck loads of material removed was recorded. The table below shows the number of dump truck loads of material removed and the number of days since the mine opened. Days (since opening) # of dump truck loads 2 45 5 53 8 60 9 60 12 67 The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 278.0 and the sum of squares of regression (SSR) was 274.3. Use these values to calculate the coefficient of determination. Round your answer to three decimal places. Select the correct answer below: 0.987 0.013 0.993

A new mine opened and the number of dump truck loads of material removed was recorded. The table below shows the number of dump truck loads of material removed and the number of days since the mine opened. Days (since opening) # of dump truck loads 2 45 5 53 8 60 9 60 12 67 The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 278.0 and the sum of squares of regression (SSR) was 274.3. Use these values to calculate the coefficient of determination. Round your answer to three decimal places. Select the correct answer below: 0.987 0.013 0.993
Transcript text: A new mine opened and the number of dump truck loads of material removed was recorded. The table below shows the number of dump truck loads of material removed and the number of days since the mine opened. \begin{tabular}{cc} Days (since opening) & \# of dump truck loads \\ 2 & 45 \\ 5 & 53 \\ 8 & 60 \\ 9 & 60 \\ 12 & 67 \end{tabular} The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 278.0 and the sum of squares of regression (SSR) was 274.3 . Use these values to calculate the coefficient of determination. Round your answer to three decimal places. Select the correct answer below: 0.987 0.013 0.993
failed

Solution

failed
failed

Solution Steps

To calculate the coefficient of determination, also known as \( R^2 \), we use the formula:

\[ R^2 = \frac{SSR}{SST} \]

where SSR is the sum of squares of regression and SST is the total sum of squares. This value indicates how well the regression line fits the data. We will compute this value using the given SSR and SST.

Step 1: Identify Given Values

We are given the total sum of squares (\( SST \)) and the sum of squares of regression (\( SSR \)). The values are:

  • \( SST = 278.0 \)
  • \( SSR = 274.3 \)
Step 2: Calculate the Coefficient of Determination

The coefficient of determination, \( R^2 \), is calculated using the formula:

\[ R^2 = \frac{SSR}{SST} \]

Substituting the given values:

\[ R^2 = \frac{274.3}{278.0} \approx 0.9867 \]

Step 3: Round the Result

Round the calculated \( R^2 \) value to three decimal places:

\[ R^2 \approx 0.987 \]

Final Answer

The coefficient of determination is \( \boxed{0.987} \). The correct answer is the first option.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Find all values (x=a) where the function is discontinuous. [f(x)=-3x/(7x-2)(2-4x)] (a=2/7, 1/2)
failedAnswered
The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 12 supermarkets from Region 1 had mean sales of 78.7 with a standard deviation of 6.7. A random sample of 16 supermarkets from Region 2 had a mean sales of 86.3 with a standard deviation of 7. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean sales per market in Region 1 and μ2 be the mean sales per market in Region 2. Use a significance level of α=0.1 for the test. Assume that the population variances are not equal and that the two populations are normally distributed. Step 1 of 4: State the null and alternative hypotheses for the test. H0: μ1 = μ2 Ha: μ1 ≠ μ2
failedAnswered
Solving a word problem using a quadratic equation with rational... The length of a rectangle is 5 m less than twice the width, and the area of the rectangle is 52 m^2. Find the dimensions of the rectangle. Length : m Width : m
failedAnswered
Add, using the rule for order of operations if necessary: -(9-2)-(10-7)=
failedAnswered
How much money does an employee working for a salary of 37,000 per year get paid every two weeks? [?] Round to the nearest whole dollar.