Question

The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, ỹ = bo + b x. for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Age 39 359 41 352 51 338 Bone Density 324 313 Table Copy Data Step 1 of 6: Find the estimated slope. Round your answer to three decimal places Answer How to Enter) 2 Points Tables Keypad

Answer 1

Ans from t = h the given data, Regression eq = ŷ = -1.600* VEY = -1680x + 490.15 . Step 1 to 48 n=5 b = | 2-4)- 41 ) = 9). next – [Enjo. => slepe, bi =(-1.620 " "The estimate slope = -10620 Step-2-6 : The Estimated intercept = ho = 399 Zly-ban bo= 420.157431 1. Step 3-6 -1.6901 +420.16 at x=o. û : +1.62060)+420.16 = 420.16. Value of the dependent variable at 1-0 Yr bo . Step-4-67 bl -1.620 Step-5-6; True . Step-6-6: The value of the coefficient of determination = x=0.9904 . P=0.9904

XValues 39 Y Values 359 352 338 324 313 51 M: 51.2 M: 337.2 Y.Dependent 39 47 63 71 55 X-Independent - Regression Line (9 = -1 62X+420.16) Estimate Calculation Summary Sum of X= 256 Sum of Y= 1686 Mean X= 51.2 Mean Y = 337.2 Sum of squares (55) = 548.8 Sum of products (SP) = -889.2 Regression Equation = ý = bx + a b= SPISSY = -889.2/548.8 = -1.62026 a = My-bMx = 337.2 - (-1.62*51.2) = 420.15743 y = -1.62026X + 420.15743 X-MX Y - My - 12.2 - 10.2 -0.2 6.8 15.8 21.8 14.8 0.8 - 13.2 -24.2 (X-MX)2 148.84 104.04 0.04 46.24 249.64 (X-MXXY - My) - 265.96 - 150.96 -0.16 -89.76 -382.36 SS: 548.8 SP: -889.2

X Values Y Values 359 Y Vabies X Values X-M -12.200 - 10.200 -0.200 6.800 15.800 Mx: 51.200 Y.M 21.800 14.800 0.800 -13.200 -24.200 My: 337.200 (X-M.)2 148.840 104.040 0.040 46.240 249.640 (Y - My)2 475.240 219.040 0.640 174.240 585.640 (X-MXXY-M, -265.960 - 150.960 -0.160 - 89.760 -382.360 Sum: 548.800 Sum: 1454.800 Sum: -889.200 Result Details & Calculation Key X Values I= 256 Mean = 51.2 EX-MX)2 = SS = 548.8 XX Values : Y Values M: Mean of X Values M: Mean of Y Values X-M, & Y - M, Deviation scores OX-M, & (Y-My Deviation Squared (x - MNY - M: Product of Deviation Scores Y Values = 1686 Mean = 337.2 ELY - My] =sSy = 1454.8 X and Y Combined N=5 ZX-MX/Y - M,) = -889.2 R Calculation r = [X-M Y-M)/VISS X55) r= -8892 / vi(548.8X1454.8)) = -0.9952 Meta Numerics (cross-check) r= -0.9952 The value of Ris -0.9952.