My Notes o Ask Your Teacher points The Nenana lce Classic in Alaska is a contest

Question

My Notes o Ask Your Teacher points The Nenana lce Classic in Alaska is a contest in which participants guess the exact day and hour when a tripod set up on the Tanana River will fall through the breaking ice Those who guess correctly split a cash prize of $300,000. Both the year and the exact breakup date have been recorded since 1917. Scientists have used this data to try to prove that global warming is occurring (ie, that the breakup date gets earlier (smaller) each year). Below are plotted the breakup dates (measured in days since Jan. 1st) against the years from 1917 to 1941. 116 y 0.2663x+134.39 R -0.1075 Year Standard Regression Table Coefficient t-Value Value Error Constant 134,386 4.782 28,103 0,0001 -1.664 0.1097 0.266 0.160 (a) What three assumptions (besides independence) are necessary for a regression? Select all that apply Linear relationship between x and y Nonlinear relationship between x and y Normally distributed y's for each x Non-normally distributed y's for each x Standard deviations of the y's are constant for each x Standard deviations of the y's are not constant for each x a Fan shape in the residuals (b) Given that the assumptions are satisfied, what is the p-value to test for a significant negative linear relationship between years and ice breakup date? 1.6640 0.0000 0.1097 0.0549 0.9451

Explanation / Answer

Solutions are given below:

(a)

The 3 assumptions necessary for the regression are:

(b)

The breakup dates are given from 1917 to 1941. So, the sample size n = 25

From the given output, t = -1.664

P-value of t at 24 df is 0.0549.

(c)

The mean breakup date predicted by the estimated regression line for the year 1935

y = 134.386 – 0.266(35) = 125.076

(d)

The actual breakup date for 1935 was 135.5642.

Residual = 125.076 – 135.5642 = - 10.49

(e)

The percent of the variability in the breakup date that can be explained by the linear relationship with year is 10.75%.

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.