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.
