Http://nm.mathforcollege.com Regression. http://nm.mathforcollege.com Applications.

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Transcript of Http://nm.mathforcollege.com Regression. http://nm.mathforcollege.com Applications.

  • http://nm.mathforcollege.comRegression

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comApplications

    http://nm.mathforcollege.com

  • Mousetrap Carhttp://nm.mathforcollege.com

    http://nm.mathforcollege.com

  • Torsional Stiffness of a Mousetrap Springhttp://nm.mathforcollege.com

    http://nm.mathforcollege.com

    Chart2

    0.188224

    0.209138

    0.230052

    0.250965

    0.313707

    (radians)

    Torque (N-m)

    Sheet1

    0.6981320.188224

    0.9599310.209138

    1.1344640.230052

    1.5707960.250965

    1.9198620.313707

    Sheet1

    (radians)

    Torque (N-m)

    Sheet2

    Sheet3

  • Stress vs Strain in a Composite Materialhttp://nm.mathforcollege.com

    http://nm.mathforcollege.com

    Chart3

    0

    306000000

    612000000

    917000000

    1223000000

    1529000000

    1835000000

    2140000000

    2446000000

    2752000000

    2767000000

    2896000000

    Strain, (m/m)

    Stress, (Pa)

    Sheet1

    0.6981320.188224

    0.9599310.209138

    1.1344640.230052

    1.5707960.2509650000

    1.9198620.3137070.1833060.00183306000000

    0.366120.0036612000000

    0.53249170.005324917000000

    0.70212230.007021223000000

    0.86715290.008671529000000

    1.024418350.0102441835000000

    1.177421400.0117742140000000

    1.32924460.013292446000000

    1.47927520.014792752000000

    1.527670.0152767000000

    1.5628960.01562896000000

    Sheet1

    0

    0

    0

    0

    0

    (radians)

    Torque (N-m)

    Sheet2

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Strain, (m/m)

    Stress, (Pa)

    Sheet3

  • A Bone Scanhttp://nm.mathforcollege.com

    http://nm.mathforcollege.com

  • Radiation intensity from Technitium-99m http://nm.mathforcollege.com

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  • Trunnion-Hub Assemblyhttp://nm.mathforcollege.com

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  • Thermal Expansion Coefficient Changes with Temperature?http://nm.mathforcollege.com

    http://nm.mathforcollege.com

    Chart1

    0.00000647

    0.00000624

    0.00000572

    0.00000509

    0.0000043

    0.00000333

    0.00000245

    Temperature, oF

    Thermal expansion coefficient, (in/in/oF)

    Sheet1

    806.47E-06

    406.24E-06

    -405.72E-06

    -1205.09E-06

    -2004.30E-06

    -2803.33E-06

    -3402.45E-06

    Sheet1

    0

    0

    0

    0

    0

    0

    0

    Temperature in degrees Fahrenheit

    Thermal expansion coefficient,

    Sheet2

    Sheet3

  • http://nm.mathforcollege.comTHE END

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comPre-Requisite Knowledge

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comThis rappers name isDa BratShawntae Harris Ke$haAshley TisdaleRebecca Black

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comClose to half of the scores in a test given to a class are above theaverage scoremedian scorestandard deviationmean score

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comThe average of the following numbers is4.07.07.510.0

    241014

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comThe average of 7 numbers is given 12.6. If 6 of the numbers are 5, 7, 9, 12, 17 and 10, the remaining number is -47.9-47.415.628.2

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comGiven y1, y2,.. yn, the standard deviation is defined as . . . .

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  • http://nm.mathforcollege.comTHE END

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.com6.03Linear Regression

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  • http://nm.mathforcollege.comGiven (x1,y1), (x2,y2),.. (xn,yn), best fitting data to y=f (x) by least squares requires minimization of

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comThe following datais regressed with least squares regression to y=a1x. The value of a1 most nearly is27.480 28.956 32.625 40.000

    x1203040y14008001300

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comA scientist finds that regressing y vs x data given below to straight-line y=a0+a1x results in the coefficient of determination, r2 for the straight-line model to be zero.The missing value for y at x=17 most nearly is-2.444 2.000 6.889 34.00

    x131117y2622?

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comA scientist finds that regressing y vs x data given below to straight-line y=a0+a1x results in the coefficient of determination, r2 for the straight-line model to be one.The missing value for y at x=17 most nearly is-2.444 2.000 6.889 34.00

    x131117y2622?

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comThe following datais regressed with least squares regression to a straight line to give y=-116+32.6x. The observed value of y at x=20 is-136 400 536

    x1203040y14008001300

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comThe following datais regressed with least squares regression to a straight line to give y=-116+32.6x. The predicted value of y at x=20 is-136 400 536

    x1203040y14008001300

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comThe following datais regressed with least squares regression to a straight line to give y=-116+32.6x. The residual of y at x=20 is-136 400 536

    x1203040y14008001300

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comTHE END

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.com6.04Nonlinear Regression

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  • http://nm.mathforcollege.comWhen transforming the data to find the constants of the regression model y=aebx to best fit (x1,y1), (x2,y2),.. (xn,yn), the sum of the square of the residuals that is minimized is

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comWhen transforming the data for stress-strain curvefor concrete in compression, where is the stress andis the strain, the model is rewritten as

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.com6.05Adequacy of Linear Regression Models

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comThe case where the coefficient of determination for regression of n data pairs to a straight line is one ifnone of data points fall exactly on the straight linethe slope of the straight line is zeroall the data points fall on the straight line

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comThe case where the coefficient of determination for regression of n data pairs to a general straight line is zero if the straight line modelhas zero intercepthas zero slope has negative slopehas equal value for intercept and the slope

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comThe coefficient of determination varies between-1 and 10 and 1-2 and 2

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comThe correlation coefficient varies between-1 and 10 and 1-2 and 2

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comIf the coefficient of determination is 0.25, and the straight line regression model is y=2-0.81x, the correlation coefficient is-0.25-0.500.000.250.50

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comIf the coefficient of determination is 0.25, and the straight line regression model is y=2-0.81x, the strength of the correlation isVery strongStrongModerateWeakVery Weak

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comIf the coefficient of determination for a regression line is 0.81, then the percentage amount of the original uncertainty in the data explained by the regression model is 91981

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comThe percentage of scaled residuals expected to be in the domain [-2,2] for an adequate regression model is859095100

    http://nm.mathforcollege.com

  • http://nm.mathforcollege.comTHE END

    http://nm.mathforcollege.com

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