residuals (degrees F) -10 0 10 20 Can the latitude of a city in the United States predict its average minimum temperature (degrees Fahrenheit) in January? A sample of cities throughout the United States was taken (excluding Alaska and Hawaii). Plots and output from a Simple Linear Regression analysis are given below. min. Jan. temperature (degrees F) 10 30 50 0 30 U.S. January Minimum Temperatures 35 40 Latitude (degrees north of equator) Residual Plot US January temperatures 30 35 40 Latitude (degrees north of equator) 45 45 Sample Quantiles -10 0 10 20 Normal Probability Plot of Residuals -2 -1 0 1 2 Theoretical Quantiles The last question on the worksheet asks about the conditions. For now, assume no transformation is necessary. Use the output below to answer the following questions. Coefficients: Estimate Std. Error t value Pr (>|t|) (Intercept) 110.8799. Latitude -2.1539 10.9660 0.2741 7.54e-11 1.47e-08 Residual standard error: 7.656 on 28 degrees of freedom Multiple R-squared: Adjusted R-squared: F-statistic: 61.76 on 1 and 28 DF, p-value: 1.466e-08 LP 7 WS Question 1 Homework Answered THREE POINTS State the null and alternative hypotheses in notation AND words in the context of the problem. (Note: for this question, you do not need to define the notation in the hypotheses since you will be writing the hypotheses in both notation and in words in the context of the problem.) TWO POINTS Using appropriate information in the output, calculate the t-statistic for the t-test to test the above null hypothesis. SHOW WORK! H B I A X x 22- 66 X Unanswered LP 7 WS Question 3 Homework ONE POINT Answered Due Today, 11:59 PM How many degrees of freedom does the t-statistic have? (Note that the sample size is not equal to the number of states!) Submit ONE POINT How many cities were in the sample? (Hint: think about the formula for the degrees of freedom for the t-statistic. Use the formula and your answer to question 3 to help you answer this question.) Type your numeric answer and submit 30 Answered Assigned as Homework O Resubmit LP 7 WS Question 5 THREE POINTS State a conclusion in the context of the problem, supported by a p-value. (Report the p-value as given in the output above.) Responses Reply Showing All Responses ordered by Newest Responses Paola Estribi an hour ago With a p value of 1.466e-08 we can reject the null hypothesis. That would mean that there is a strong evidence that the latitude of a city in the United States is a significant predictor of its average minimum temperature in January. Comments 0 1 LP 7 WS Question 6 Homework Unanswered FOUR POINTS Construct AND interpret (in the context of the problem) a 95% confidence interval for the slope of the regression line. SHOW WORK! H B I A X x 66 X Unanswered LP 7 WS Question 7 == Homework Unanswered Submit TWO POINTS Corvallis is located at 44.56 degrees north of the equator. What average minimum January temperature does the model predict for Corvallis? SHOW WORK. (Don't forget to include units in your answer!) (==) LP 7 WS Question 8 Homework Unanswered TWO POINTS The actual average minimum temperature in January in Corvallis is 33.2 degrees. Calculate Corvallis's residual. SHOW WORK! (Don't forget to include units in your answer!) H B I A X - Unanswered Assigned as Homework x 22- 66 X Submit LP 7 WS Question 9 ONE POINT Based on the residual calculated in question 8, how well does the model "work" for Corvallis (i.e. accurately predict the average minimum temperature in January)? Briefly explain. LP 7 WS Question 9 ONE POINT Based on the residual calculated in question 8, how well does the model "work" for Corvallis (i.e. accurately minimum temperature in January)? Briefly explain. Responses Reply ssigned as Homework Showing All Responses ordered b LP 7 WS Question 10 ONE POINT Why doesn't the model "work" well for Corvallis? (That is, what geographical feature would explain why Co residual? This is not an easy question to answer, but do your best to think about what geographical feature different than other cities at the same latitude in Corvallis?) Responses Reply ssigned as Homework Showing All Responses ordered b LP 7 WS Question 11 THREE POINTS Discuss if you feel the linearity, constant variation, and normality conditions are satisfied. In your discussio