Question

With Obesity on the rise, a Doctor wants to see if there is a linear relationship between the Age and Weight and estimating a person's Systolic Blood Pressure. Using the Estimated Regression equation, Estimate Systolic BP when some if 39 years old and they weigh 143 pound.
A. 114.785.
B. 115.532.
C. 122.471.
D. 112.569
Systolic BP Age in Yrs. Weight in lbs.
132 52
143 59 184
153 67 194
162 73 168
154 64 196
168 74 220
137 54 188
149 61 188
159 65 207
128 46 167
166 72 217
135 52 187
148 61 161
148 61 189
161 65 205
126 45 161
167 75 215

Answer 1

Answer:

112.569 ( D )

Step-by-step explanation:

Applying the estimated Regression Equation

y = b1X1 + b2X2 + a

b1 = ((SPX1Y)*(SSX2)-(SPX1X2)*(SPX2Y)) / ((SSX1)*(SSX2)-(SPX1X2)*(SPX1X2)) = 596494.5/635355.88 = 0.93884

b2 = ((SPX2Y)*(SSX1)-(SPX1X2)*(SPX1Y)) / ((SSX1)*(SSX2)-(SPX1X2)*(SPX1X2)) = 196481.5/635355.88 = 0.30925

a = MY - b1MX1 - b2MX2 = 149.25 - (0.94*61.31) - (0.31*193.88) = 31.73252

y = 0.939X1 + 0.309X2 + 31.733

For x1 ( age ) =39, and  x2(weight) =143

y = (0.93884*39) + (0.30925*143) + 31.73252= 112.569

where

Sum of X1 = 981

Sum of X2 = 3102

Sum of Y = 2388

Mean X1 = 61.3125

Mean X2 = 193.875

Mean Y = 149.25

attached is the Tabular calculation of the required values needed for estimated regression equation