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
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Solution

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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.

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