An agricultural scientist is interested in studying the relationship between the

Question

An agricultural scientist is interested in studying the relationship between the trunk circumference of apple trees, X (in inches) and the apple yield, Y (in pounds). He randomly selects 80 trees, records the values of X and Y, constructs a scatterplot of the data and calculates the summaries given below. Suppose that the scatterplot reveals the relationship to be linear. sigma x = 3, 280 sigma x^2 = 142, 380 sigma xy = 208, 574 sigma y = 4, 960 sigma y^2 = 318.896 Calculate the equation of the least-squares regression line. (a) y = 34.94 + 0.660x (b) y = 89.06 + 0.660x (c) y = 236.800 + 1.440x (d) y = 12.60 + 0.458x

Explanation / Answer

here SSx=142380-(3280)2/80 =7900

SSy=318896-4960^2/80=11376

Sxy=208574-3280*4960/80=5214

hence b1 =Sxy/SSx =0.66

and b0=Ybar-Xbar*b0=4960/80 -3280*0.66/80=34.94

hence option A is correct

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