Please see the detailed homework policy document for information about homework formatting, submission, and grading.


Exercise 1

The above (simulated, and not the same as the previous homework) data shows the relationship between sleep (in hours) and weight (in kilograms) of a random sample of adult males on a particular night. A simple linear regression model was fit to this data. The fitted line is added to the above plot.

## 
## Call:
## lm(formula = sleep ~ wt, data = sleep_wt_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9405 -0.5596 -0.0905  0.6341  1.5812 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 13.75851    2.71887    5.06 8.15e-05 ***
## wt          -0.06833    0.02969      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.951 on 18 degrees of freedom
## Multiple R-squared:  0.2274, Adjusted R-squared:  0.1845 
## F-statistic: 5.297 on 1 and 18 DF,  p-value: 0.03352

Some evil professor has hacked R and ruined the output from the summary() function. Use what information is provided to carry out the test

\[ H_0: \beta_1 = 0 \quad \text{vs} \quad H_1: \beta_1 \neq 0 \]

Report:


Exercise 2

Using only the information provided in Exercise 1, create 95% confidence intervals for \(\beta_0\) and \(\beta_1\).


Exercise 3

The above (simulated, and not the same as the previous homework) data shows the relationship between exam scores and sleep (in hours) for a random sample of students in a large statistics course. A simple linear regression model was fit to this data. The fitted line is added to the above plot.

Use the above statistics to calculate:


Exercise 4

The following three plots show: