Question Help The table gives performance data for a boat powered by a certain o

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Question Help The table gives performance data for a boat powered by a certain outboard motor. Find a quadratic regression model (y ax +bxc) for boat speed n,500 miles per hour) as a function of engine speed (in revolutions per minute) Estimate the boat speed at an engine speed of 3,200 revolutions per minute rpm mph 4.5 2,000 5.7 2.500 7.8 3,000 9.6 3,500 13.4 Complete the quadratic regression calculator screen below. QuadReg y - ax bx+c aE-6 (Round to the nearest tenth as needed.) bRound to five decimal places as needed.) Round to the nearest tenth as needed) What is the estimated boat speed at an engine speed of 3,200 revolutions per minute? mph (Use the answers from the previous step to find this answer. Round to the nearest tenth as needed.)

Explanation / Answer

The statistical software output for this problem is:

Polynomial Regression Results:
Dependent Variable: mph
Independent Variable: rpm
mph = 5.4 + -0.00266 X + 0.0000014 X^2

Parameter estimates

Analysis of variance table for polynomial regression model:

Summary of fit:
Root MSE: 0.38470768
R-squared: 0.994
R-squared (adjusted): 0.9879

Predicted values:

Hence,

a = 1.4 E - 6

b = -0.00266

c = 5.4

Estimated boat speed for 3200 revolutions per minute = 11.2

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 5.4 2.4478329 0 2 2.206033 0.1581 X -0.00266 0.0020706935 0 2 -1.2845938 0.3276 X^2 0.0000014 4.1126981e-7 0 2 3.4040913 0.0765

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