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# (Solved) MATH225 Week 8 Assignment Coefficient of Determination

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Question

A medical experiment on tumor growth gives the following data table.

 x y 57 38 61 50 63 76 68 97 72 113

The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) wasÂ 3922.8Â and the sum of squares of regression (SSR) wasÂ 3789.0. CalculateÂ R2, rounded to three decimal places.

Question

A scientific study on mesothelioma caused by asbestos gives the following data table.

 Micrograms of asbestos inhaled Area of scar tissue (cm2) 58 162 62 189 63 188 67 215 70 184

Using technology, it was determined that the total sum of squaresÂ (SST)Â wasÂ 1421.2Â and the sum of squaresÂ due to errorÂ (SSE)Â wasÂ 903.51. CalculateÂ R2Â and determine its meaning. Round your answer to four decimal places.

R2=0.3643

• Therefore,Â 36.43%Â of the variation in the observedÂ y-values can be explained by the estimated regression equation.

R2=0.3643

• Therefore,Â 0.3643%Â of the variation in the observedÂ y-valuesÂ can be explained by the estimated regression equation.

R2=0.6357

• Therefore,Â 63.57%Â of the variation in the observedÂ y-values can be explained by the estimated regression equation.

R2=0.6357

• Therefore, 0.6357% of the variation in observed y-values can be explained by the estimated regression equation.

Question

A scientific study on speed limits gives the following data table.

 Average speed limit Average annual fatalities 25 16 27 29 29 38 32 71 35 93

Using technology, it was determined that the total sum of squaresÂ (SST)Â wasÂ 4029.2, the sum of squares regressionÂ (SSR)Â wasÂ 3968.4, and the sum of squares due to errorÂ (SSE)Â wasÂ 60.835. CalculateÂ R2Â and determine its meaning. Round your answer to four decimal places

R2=0.0153

• Therefore, 1.53% of the variation in the observed y-values can be explained by the estimated regression equation.

R2=0.9849

• Therefore,Â 98.49%Â of the variation in the observedÂ y-valuesÂ can be explained by the estimated regression equation.

R2=0.0151

• Therefore,Â 1.51%Â of the variation in the observedÂ y-values can be explained by the estimated regression equation.

R2=1.0153

• Therefore,Â 10.153%Â of the variation in the observedÂ y-valuesÂ can be explained by the estimated regression equation.

R2=0.9849

• Therefore,Â 98.49%Â of the variation in the observedÂ y-valuesÂ can be explained by the estimated regression equation.

Question

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

A least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) wasÂ 278.0Â and the sum of squares of regression (SSR) wasÂ 274.3. Use these values to calculate the coefficient of determination. Round your answer to three decimal places

• 0.987
• 0.013
• 0.993

Question

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 6 54 9 78 14 92 17 86 21 121

A least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) wasÂ 2349Â and the sum of squares of error (SSE) wasÂ 329. Use these values to calculate the coefficient of determination. Round your answer to three decimal places