Fitting a straight line to a set of data yields the following prediction line. C
ID: 3243529 • Letter: F
Question
Fitting a straight line to a set of data yields the following prediction line. Complete (a) through (c) below. Y_i cap = 17 - 0.8X_i Interpret the meaning of the Y-intercept, b_0. Choose the correct answer below. The Y-intercept, b_0 = -0.8, implies that when the value of X is 0, the mean value of Y is -0.8. The Y intercept, b_0 = 17, implies that when the value of X is 0, the mean value of Y is 17. The Y-intercept, b_0 = 17, implies that for each increase of 1 unit in X, the value of Y is expected to increase by 17 units. The Y-intercept, b_0 = 17, implies that the average value of Y is 17. Interpret the meaning of the slope, b_1. Choose the correct answer below. The slope, b_1 = -0.8, implies that the average value of Y is -0.8. The slope, b_1 = 17 implies that for each increase of 1 unit in X, the value of Y is expected to increase by 17 units. The slope, b_1 = -0.8, implies that for each increase of 1 unit in X, the value of Y is estimated to decrease by 0.8 units. The slope, b_1 = 0.8, implies that for each increase of 1 unit in X, the value of Y is expected to increase by 0.8 units. Predict the mean value of Y for X = 4 ? Y_i cap = (Type an integer or a decimal.)Explanation / Answer
y = 17 -0.8 Xi
a) b0 = 17
it is interpreted as mean value of y when x =0
so option B) is correct
b) b1 = -0.8
it is interpreted as change in y when we change the x by 1 unit
since b1 <0 , y will decrease by 0.8 units
hence option C) is correct
c) Y = 17-0.8*4 = 13.8
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