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given the following data, compute a regression run, save the equation and then use the formula to compute the value of the dependent variable when the value of x is 15. (please round your answers to two decimal places)



Answer :

contexto1019

To perform a regression analysis, we need to compute the values for the slope (b) and the intercept (a) of the regression line. The slope is given by:

  • $ b = \frac{\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^n (x_i - \bar{x})^2} $

Where $\bar{x}$ and $\bar{y}$ are the means of the X and Y variables, respectively, and n is the number of observations.

The intercept is given by:

  • $ a = \bar{y} - b\bar{x} $

Using the given data, we can compute the slope and intercept as follows:

  • $ \begin{aligned} b &= \frac{\sum_{i=1}^{10} (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^{10} (x_i - \bar{x})^2} \ &= \frac{(30-17.1)(67-66.6) + (3-17.1)(57-66.6) + \dots + (17-17.1)(70-66.6)}{(30-17.1)^2 + (3-17.1)^2 + \dots + (17-17.1)^2} \ &= \frac{260}{719} \ &= 0.36 \end{aligned} $

  • $ \begin{aligned} a &= \bar{y} - b\bar{x} \ &= 66.6 - 0.36 \cdot 17.1 \ &= 50.4 \end{aligned} $

The regression equation is, therefore:

  • $ \hat{y} = 50.4 + 0.36x $

To compute the value of the dependent variable when the value of X is 15, we plug this value into the regression equation:

  • $ \hat{y} = 50.4 + 0.36 \cdot 15 = 60.6 $

The value of the dependent variable when the value of X is 15 is approximately 60.6.

Learn more about Regression Equations here:

https://brainly.com/question/25987747

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Complete Question:

Given the following data, compute a regression run, save the equation and then use the formula to compute the value of the dependent variable when the value of X is 15. (Please round your answers to two decimal places)

Х : 30 3 14 22 16 5 18 32 4 17

Y : 67 57  53  78  90  97  92  44 58 70

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