nput variable, consider the case of using cubic splines with 123 knots. Looking at the spline model as a linear regression model with the input variables corresponding to (some) spline basis functions, if you run an exhaustive best subset selection in order to to select the best subset with 5 coefficients, how many different models would you

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Is It Getting Harder to Win a Hot Dog Eating Contest?Every Fourth of July, Nathan’s Famous in New York City holds a hot dog eating contest. The table below shows the winning number of hot dogs and buns eaten every year from 2002 to 2015, and the data are also available in HotDogs. The figure below shows the scatterplot with the regression line. Year     Hot Dogs 2015   62 2014   61 2013   69 2012   68 2011   62 2010   54 2009   68 2008   59 2007   66 2006   54 2005   49 2004   54 2003   45 2002     50 Winning number of hot dogs in the hot dog eating contest Winning number of hot dogs and buns Click here for the dataset associated with this question.   (a) Is the trend in the data mostly positive or negative?     Positive   Negative   (b) Using the figure provided, is the residual larger in 2007 or 2008?Choose the answer from the menu in accordance to item (b) of the question statement  20072008 Is the residual positive or…

The​ least-squares regression equation is y=784.6x+12,431 where y is the median income and x is the percentage of 25 years and older with at least a​ bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7962.  In a particular​ region, 26.5 percent of adults 25 years and older have at least a​ bachelor's degree. The median income in this region is ​$29,889. Is this income higher or lower than what you would​ expect? Why?