Analyzing Registered and Casual Users: Linear Regression, T-Test, and ANOVA Results

1)
We have taken the Registered user as the dependent variable and Casual users as the independent
variable.
Now when we are plotting the simple linear regression then we are taking the hypothesis that
H0: The coefficients are not significant in other words we can say that Registered user does not
depends on the Casual users. So the betas are insignificant
H1: The coefficients are significant which means the registered user are dependent on the Casual
users. The betas are significant
Call:
lm(formula = Registered ~ Casual, data = bikedata)
Residuals:
Min 1Q Median 3Q Max
-2280.1 -537.1 -138.7 488.7 1799.2
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.027e+03 1.539e+02 6.673 1.5e-09 ***
Casual 1.329e+00 9.458e-02 14.054 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 780 on 98 degrees of freedom
Multiple R-squared: 0.6684, Adjusted R-squared: 0.665
F-statistic: 197.5 on 1 and 98 DF, p-value: < 2.2e-16
As we can see the p values are much less than 0.05 so both the intercept and the beta are
significant which means registered users is dependent on the casual users.
The different plots which we obtained are

2)
We can use two sample t test to compare the Total users in year 2011 and year 2012.
Null Hypothesis: Means are equal for both year 2011 and year 2012
Alternate Hypothesis: Means are not equal for year 2011 nad year 2012