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1 month ago

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Can we predict how fast a tennis player can hit a serve from the playerâs height? The following computer output and scatterplot

describe the regression of fastest serve speed (in kilometers per hour) and the height (in meters) of 21 current male professional tennis players.
a. Describe the relationship between height and fastest serve speed for these tennis players.
b. Write the equation of the least-squares regression line. Define any variables used.
c. Interpret the value "R-sq = 27.7%".
d. What is the slope of the least-squares regression line? Interpret this value.
e. Predict the fastest serve of a professional tennis player whose is 1.7 meters tall. Comment on the reliability of this prediction.
f. What is the value of the correlation between height and fastest serve speed? Interpret this value.
g. Calculate the residual for the player that is 2.06 meters tall and has a fastest serve speed of 230 km/hr. Interpret this value.

1 answer:

lawyer [12.5K]1 month ago

3 0

Complete question:

The output from the computer and the scatter plot related to the question are in the image provided.

Answer:

Please refer to the explanation

Step-by-step explanation:

A.) Connection between height and fastest serve speed:

The scatter plot and the R value, derived from the square root of R², indicate the following:

R = √27.7%

R = 0.5263 = 52.63%; this suggests a moderately strong positive correlation between height and serve speed.

B.)

Writing the equation for the least square regression line:

Based on the computer's output and the previously mentioned scatter plot:

Recall:

y = mx + c

y = predicted variable (fastest serve)

m = slope

x = predictor variable (height)

c = intercept

y = 84.98x + 68.81

C.) The height explains 27.7% of the variability in fastest serves, with the rest being attributable to other factors.

D.) For a tennis player measuring 1.7m:

y = 84.98x + 68.81

y = 84.98(1.7) + 68.81

y = 213.276 km/hr

E.)

R = √27.7%

R = 0.5263 = 52.63%; this indicates a moderately strong positive relationship between height and serve speed.

F.)

If height = 2.06m, then:

y = 84.98(2.06) + 68.81

y = 243.8688 km/hr

Residual = Actual - predicted

Actual = 230; predicted = 243.8688

Residual = 230 - 243.8688

Residual = -13.8688

Thus, the prediction overestimates the fastest serve speed of a player standing 2.06 m tall by -13.8688 km/hr.

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