How does the maximum swim speed is affected by the length/height?
Logic for analysis:
We want to predict the value of the dependent variable which is speed based on the independent variables (length and height), here we will use regression analysis. We can try three analyses in order to find the correct model:
1. Regression model with speed as dependent variable and length as independent variable
2. Regression model with speed as dependent variable and height as independent variable
3. Regression model with speed as dependent variable and length and height as independent variables

Analysis 1: Regression model with speed as dependent variable and length as independent variable
Null Hypothesis (Ho): The regression model is not significant, and it is not able to predict the dependent variable. It means there is no statistically significant association between speed and length.
Alternative Hypothesis (Ha): The regression model is significant, and it is able to predict the dependent variable. It means there is a statistically significant association between speed and length.
Level of significance = 0.05
Decision Rule: Reject Ho if p-value is smaller than the level of significance.
R Code for Analysis:
fit <- lm(speed ~ length, data=data)
summary(fit) # show results
R Output is given below:
Call:
lm(formula = speed ~ length, data = data)

Residuals:
Min 1Q Median 3Q Max
-5.1777 -1.6722 -0.0035 1.7171 4.9536

#1. For a confidence level of 96%, find the critical value #2. For...