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melania is tracking her running training program. the table gives her 5k run time at the end of each month. month time (in minutes) 1 47 2 43 3 39 4 36 5 35 6 33 what is the equation for the line of best fit, where x represents the month and y-hat represents the predicted time? y hat equals 33.6 plus 2.77 times x y hat equals 48.5 plus 2.77 times x y hat equals 33.6 minus 2.77 times x

Respuesta :

The required regression  equation for the line of best fit, where x represents the month and y-hat represents the predicted time is;

y = -2.78x + 48.5

How to find the regression equation?

A regression equation is defined as the equation that is used in stats to find out what relationship, if any, exists between sets of data

From the given table, let x represents the month and y represents the time. Thus;

Mean of x; x-bar = (1+2+3+4+5+6)/6 = 21/6

x-bar = 3.5

Mean of y; y-bar = (47+43+39+36+35+33)/6

y-bar = 233/6 = 38.83

∑x = 21

∑y = 233

Using statistics calculator;

Sum of squares (SSX) = 17.5

Sum of products (SP) = -48.5

The general form of a regression Equation is;

y-bar = bx-bar + a

Where;

b = SP/SSX

= -48.5/17.5

= -2.77143

a = y-bar - b(x-bar) = 38.83 - (-2.77×3.5) = 48.53333

y = -2.78x + 48.5

Thus, the required regression equation is y = -2.78x + 48.5 for the line of best fit.

Read more about regression equation at; https://brainly.com/question/25987747

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