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 2 years ago

In the 2016 Olympics in Rio, after the 50 m freestyle competition, a problem with the...

In the 2016 Olympics in Rio, after the 50 m freestyle competition, a problem with the pool was found. In lane 1 there was a gentle 1.2 cm/s current flowing in the direction that the swimmers were going, while in lane 8 there was a current of the same speed but directed opposite to the swimmers' direction. Suppose a swimmer could swim the 50.0 m in 25.0 s in the absence of any current. Part A: How would the time...

You wish to dispose of 100 mL of 0.1 M sodium phosphate buffer, pH 4.5. Where...

You wish to dispose of 100 mL of 0.1 M sodium phosphate buffer, pH 4.5. Where will you do this? Select all correct answers in list. Mercury Spill Kit Base Compatible Aqueous Waste Acid Compatible Mercury Waste Sanitary Sewer Acid Compatible Organic Waste Acid Compatible Acutely Hazardous Waste Acid Compatible Aqueous Waste Concentrated Nitric Acid Waste Base Compatible Mercury Waste Organic Solid Waste Base Compatible Acutely Hazardous Waste Inorganic Solid Waste Base Compatible Organic Waste

You wish to prepare 50.00 mL of 0.0600 M NH3 from concentrated ammonia (15.28 M) by...

You wish to prepare 50.00 mL of 0.0600 M NH3 from concentrated ammonia (15.28 M) by serial dilution using a 50 mL volumetric flasks, a 1.00 mL volumetric pipet, and a 10.00 mL graduated pipet. For the first dilution in the series, 1 mL of concentrated ammonia is added to a 50.00 volumetric flask and then filled to the line. The solution is mixed thoroughly, poured into a beaker, and then used to make the second solution in the series....

In which of the following cases would you be able to predict with certainty the change...

In which of the following cases would you be able to predict with certainty the change in the equilibrium price? There is more than one answer to this question. You must mark all of the correct answers to receive full credit for this question. There is a decrease in demand. There is a decrease in demand and an increase in supply. There is an increase in demand and an increase in supply. There is an increase in supply. There is...

How are you able to predict the future and explain the past using the IS-LM?

A 100. ml sample of 0.10 M HCl is mixed with 50. ml of 0.10 M...

A 100. ml sample of 0.10 M HCl is mixed with 50. ml of 0.10 M NH3. What is the resulting pH? Thank you!

You are seeing a 50-year-old female for her annual physical. She is a long time patient...

You are seeing a 50-year-old female for her annual physical. She is a long time patient in the practice that you have just joined. She has no complaints and states that she feels well. Her past medical history is notable for "borderline hypertension" and obesity. Last year, her lipid panel was acceptable for someone without known risk factors or coronary artery disease. TC 214; Trig 202; HDL 32; LDL 146 [reading in summer of 2015, fasting]. Her brother and mum...

(1a) Suppose you wish to predict Yi having observed Xi , but you tie your hands...

(1a) Suppose you wish to predict Yi having observed Xi , but you tie your hands to prediction rules of the form f(Xi) = g1Xi for some constant g1. Derive a formula for coefficient γ1 that minimizes the mean square prediction error M(g1) = E[(Yi − g1Xi) 2 ]. (1b) Now suppose you wish to estimate a regression model of the form Yi = β1Xi +ui . Derive a formula relating β1 and γ1. (1c) Using your answer to part...

You bungee jump from a point 50 [m] off the ground with a mass of 75...

You bungee jump from a point 50 [m] off the ground with a mass of 75 [kg] using a bungee cord with an unstretched length of 16 [m] and a spring constant of 55 [N/m]. Will you hit the ground and at what speed? If you will not hit the ground, how close to the ground do you come to a stop?

berdine has developed cataracts in both eyes preventing her from being able to identify een her...

berdine has developed cataracts in both eyes preventing her from being able to identify een her mothers face, berdine most clearly suffers a deficiency in A)perceotual set b)sensory adaptation c)bottom-up processing