Question

In: Statistics and Probability

Height vs Weight - Erroneous Data: You will need to use software to answer these questions....

Height vs Weight - Erroneous Data: You will need to use software to answer these questions.

Below is the scatterplot and corresponding data for the height and weight of 11 randomly selected adults. You should notice something odd about the last entry.

         
index height (x) weight (y)
inches pounds
1 60 120
2 72 200
3 65 130
4 71 205
5 67 180
6 70 180
7 69 193
8 71 195
9 63 115
10 62 140
11 5.5 160

You should be able copy and paste the data by highlighting the entire table.

Answer the following questions regarding the relationship.

(a) Using all 11 data pairs for height and weight, calculate the slope and y-intercept of the regression line. Round the slope to 2 decimal places and the y-intercept to 1 decimal place.
ŷ =  x +

(b) Using the regression equation from part (a), estimate the weight of a person who is 62 inches tall. Round your answer to one decimal place.
ŷ =  pounds

(c) Using only the first 10 data pairs for height and weight, calculate the slope and y-intercept of the regression line. Round the slope to 2 decimal places and the y-intercept to 1 decimal place.
ŷ =  x +

(d) Using the regression equation from part (c), estimate the weight of a person who is 62 inches tall. Round your answer to one decimal place.
ŷ =  pounds

(e) Which statement(s) explain this situation?

The height for the last data pair must be an error.The erroneous value from the last data pair drastically changed the regression equation.    Including the last data pair made the slope closer to zero.The prediction from part (d) should be more accurate than the prediction from part (b).All of these are valid statements.

Solutions

Expert Solution

a.

Sum of X = 675.5
Sum of Y = 1818
Mean X = 61.4091
Mean Y = 165.2727
Sum of squares (SSX) = 3602.4091
Sum of products (SP) = 1590.2727

Regression Equation = ŷ = bX + a

b = SP/SSX = 1590.27/3602.41 = 0.44

a = MY - bMX = 165.27 - (0.44*61.41) = 138.2

ŷ = 0.44X + 138.2

b. For x=62, ŷ = 0.44*62 + 138.2=165.5

c.

Sum of X = 670
Sum of Y = 1658
Mean X = 67
Mean Y = 165.8
Sum of squares (SSX) = 164
Sum of products (SP) = 1266

Regression Equation = ŷ = bX + a

b = SP/SSX = 1266/164 = 7.72

a = MY - bMX = 165.8 - (7.72*67) = -351.4

ŷ = 7.72X - 351.4

d. For x=62, ŷ = 7.72*62 - 351.4=127.2

e. The erroneous value from the last data pair drastically changed the regression equation.

orchestra answered 2 years ago
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