Question

In: Statistics and Probability

I ONLY NEED PART "e" and "g", parts "a" to "d" have been answered and included...

I ONLY NEED PART "e" and "g", parts "a" to "d" have been answered and included for reference.

3. Here are the world record times for women in the 10,000-meter run over several years.

Record Year

1979

1981

1981

1981

1982

1983

1983

1984

1985

1986

Time (in seconds)

1972.5

1950.8

1972.5

1937.2

1895.3

1895.0

1887.6

1873.8

1859.4

1813.7
  1. Which is the explanatory variable, and which is the response variable?

The explanatory variable is Record Year and the response variable is Time.

  1. Make a scatterplot of these data. (You do not have to include your graph.) Describe what you see (form, direction, strength, outliers).

form = linear, direction = negative, strength = strong, outliers = No

  1. Write the equation of the regression line for predicting record time from year.

y = -23.301 x + 48,100.478

  1. What is the meaning of the slope of your line? What are the units of the slope?

For every additional year, the record Time will decrease by 23.301.

e. What percent of the observed variation in the record times can be explained by your model?

g. The record from 1986 was broken in 1993, with a time of 1771.8 seconds. The record from 1986 was finally broken in 2016, with a time of 1757.5 seconds. Make a new scatterplot of these data, including these two additional points. Describe what you see. Would you use the equation you wrote in part c. to describe this new, bigger data set? Why or why not?

Solutions

Expert Solution

(e)

Percentage of variance in y that is explained by this model is given by R^2, which is given by

Therefore, percentage of variance in y that is explained by this model is given by 0.9113402.

(f)

Scatter plot alongwith the new observations (in black and purple colour) is shown below

Observation: The new observations do not lie in the same line of scatter as the older observations.

Hence, the equaton in part (c) won't be useful for the bigger dataset reason being that the new observations are leverage points and including them would change the slope of the equation considerably.

Hope this was useful. Please leave back any comment.

orchestra answered 1 year ago
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