Question

In: Statistics and Probability

You wish to be able to predict a swimmer’s 100 m freestyle time from her 50...

You wish to be able to predict a swimmer’s 100 m freestyle time from her 50 m freestyle time. Here are the 50 m and 100 m free times for 20 competitive female swimmers.

50 m Free 100 m Free

24.89 50.35

26.04 52.17

25.18 50.87

25.24 50.23

25.68 51.66

25.02 49.85

26.03 52.15

25.96 51.30

25.23 49.88

25.10 50.00

25.60 50.46

25.35 51.09

24.70 49.26

25.49 51.11

25.95 51.56

25.61 51.86

25.64 51.24

26.04 51.73

25.01 50.03

24.92 49.46

Have SPSS make a scatter plot of this data, with the regression line and bounding lines superimposed. Include the plot in your response.
Ask SPSS to find the correlation between the times.
Describe and test the hypothesis of meaningful prediction, considering both slope and correlation. Include any appropriate SPSS output in your response.
Predict the 100 m free times for three competitive female swimmers with 50 m free times of 24.9, 25.4, and 26.6 respectively.
Predict the 100 m free time for a male swimmer with a 50 m free time of 22.1.
Discuss the amount of credibility you place in these predictions.

Expert Solution

The scatterplot using SPSS is:

The SPSS output is:

The hypothesis being tested is:

H₀: β₁ = 0

H₁: β₁ ≠ 0

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

The regression equation is:

y = 2.910 + 1.883*x

Put x = 24.9, y = 2.910 + 1.883*24.9 = 49.8

Put x = 25.4, y = 2.910 + 1.883*25.4 = 50.7

Put x = 26.6, y = 2.910 + 1.883*26.6 = 53.0

Put x = 22.1, y = 2.910 + 1.883*22.1 = 44.5

80.7% of the variability in the model is explained, thus, this model can be used to make these predictions.

orchestra answered 1 year ago

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