Question

5. In an area of the Midwest, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre).

Rain (inches) 10.5 8.8 13.4 12.5 18.8 10.3 7.0 15.6 16.0

Yield (bushels/acre) 50.5 46.2 58.8 59.0 82.4 49.2 31.9 76.0 78.8

Which is the best predicted value for y given x = 7.1? Assume that the variables x and y have a significant correlation.

A. 35.4

B. 35.2

C. 35.7

D. 35.9

Answer 1

We will find an equation of the regression line in 4 steps.

Step 1: Find as it was done in the table below.

X	Y	X⋅Y	X⋅X
10.5	50.5	530.25	110.25
8.8	46.2	406.56	77.44
13.4	58.8	787.92	179.56
12.5	59	737.5	156.25
18.8	82.4	1549.12	353.44
10.3	49.2	506.76	106.09
7	31.9	223.3	49
15.6	76	1185.6	243.36
16	78.8	1260.8	256

Step 2: Find the sum of every column:

Step 3: Use the following equations to find a and b:

Step 4: Substitute a and b in regression equation formula

Which is the best predicted value for y given x = 7.1

y=4.267+4.379*7.1

y=35.4