Every spring the city of Nenana, Alaska hosts a contest in which participants try to guess the exact minute that a wooden tripod placed on the frozen Tanana river will fall through the breaking ice.

The contest started in 1917 as a diversion for railroad engineers, with a jackpot of $800 for the closest guess. It has grown into an event in which hundreds of thousands of entrants submit their estimates on theinternet. The 2021 prize money for the closest guess was $233,591.

Because so much money and interest depends on the time of ice breakup, it has been recorded to the nearest minute with great accuracy ever since 1917. And because a standard measure of breakup has been used throughout this time, the data are consistent. We will investigate if we can use the past data to make a good prediction of the next breakup time.

This Excel fileNenana Ice Breakup Timesshows the data from the beginning of the contest through 2021. To acquire some understanding of the data you should make a scatterplot of the data with "Year (since 1900)" on the x-axis and "Day Number" on the y-axis.

Column C lists the ice breakup for each year as the number of days from the beginning of that year starting with January 1 as day 1. For example, the breakup in 1998 is listed as 109.7045 days from January 1, 1998. Day 109 of 1998 is April 19; 0.7045 days is an additional 16.908 hours, or 16 hours and 54 minutes. Therefore the breakup in 1998 occurred on April 20, 4:54 PM. As another example, in 1992 (a leap year), the breakup time is listed as 134.2684. Day number 134 in 1992 is May 13; 0.2684 days is an additional 6.4416 hours, or 6 hours and 26 minutes. Therefore the breakup occurred on May 14, 6:26 AM.

Question 1. Exclude the data for 2021 and find the slope and intercept of the least squares line using "Year (since 1900)" as the predictor variable (x-variable) and "Day Number" as the response variable (y-variable).

slope (use 4 decimal places; don't forget to exclude the data for 2021) intercept (use 4 decimal places; don't forget to exclude the data for 2021)

Question 2. Use the least squares line to predict the ice breakup time in 2021.

May 2, 1:40 AMMay 5, 2:16 PM April 30, 1:12 AMMay 1, 8:41 PMApril 20, 9:08 AMApril 20, 7:09 PMApril 25, 10:43 AM

Question 3. By how many days and hours, to the nearest whole hour, does yourpredictedice breakup time for 2021 differ from theactualice breakup time for 2021?

days hours.

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