Question

The table gives the amount of money (in dollars) spent on football by a major university. Letting 2 represent the number of years since 2005, and letting y represent the amount of money spent on football, in thousands of dollars, use the regression capabilities of a graphing calculator to find the equation of the line of best fit. Round values off to the nearest hundredth. Then, use your equation to make the following predictions. Year Dollars spent on football 2005 177,000 2006 192,000 2007 207,000 2008 227.000 2009 243,000 2010 292,000 The equation of the line of best fit is: Hint Predict the amount of money that will be spent on football in the year 2022. $ s Predict the amount of money that will be spent on football in the year 2041.​

Answer 1

The line of best-fit is of:

$y = 21.37x + 169.58$

Using the line:

• The estimate for the spending in 2022 is of $532,870.
• The estimate for the spending in 2022 is of $938,900.

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The line of best fit, for the amount spent on football in x years after 2005 is given by:

$y = mx + b$

• The slope is:

$m = \frac{\sum_{i = 1}^{6} (x_i - \overline{x})(y_i - \overline{y})}{\sum_{i = 1}^{6} (x_i - \overline{x})^2}$

• We consider the means as $\overline{x}$ and $\overline{y}$. They are used to find the coefficient b.
• Also x is the number of years after 2005, thus it's measures are 0, 1, 2, 3, 4 and 5, that is, $x_1 = 0, ..., x_5 = 5$.

• y is measured in thousands, thus $y_1 = 177, ... y_6 = 292$.

The means are:

$\overline{x} = \frac{0 + 1 + 2 + 3 + 4 + 5}{6} = 2.5$

$\overline{y} = \frac{177 + 192 + 207 + 227 + 243 + 292}{6} = 223$

Finding the slope:

$\sum_{i = 1}^{6} (x_i - \overline{x})(y_i - \overline{y}) = 374$

${\sum_{i = 1}^{6} (x_i - \overline{x})^2} = 17.5$

$m = \frac{\sum_{i = 1}^{6} (x_i - \overline{x})(y_i - \overline{y})}{\sum_{i = 1}^{6} (x_i - \overline{x})^2} = \frac{374}{17.5} = 21.37$

Now finding b:

$y = 21.37x + b$

Replacing the means:

$223 = 21.37(2.5) + b$

$b = 169.58$

Thus, the line of best fit is:

$y(x) = 21.37x + 169.58$

2022 is 2022 - 2005 = 17 years after 2005, thus, the estimate for 2022 is of:

$y(17) = 21.37(17) + 169.58 = 532.87$

Following the same logic, the estimate for 2041 is of:

$y(36) = 21.37(36) + 169.58 = 938.9$

A similar problem is given at brainly.com/question/16793283