Question

a. obtain the equation of the estimated regression line and use it to calculate a point prediction of ammonium concentration for a future observation made when ammonium concentration is 25ml/h.

Answer 1

The  equation of the regression line is  $\bar{y}$=9.1006+(-0.2157)x and the point prediction of ammonium concentration for 25ml/h is  $\bar{y}$=3.7081

What is meant by regression line?

A regression line is an approximation of the line that describes the true, but unknown, linear connection between two variables. The regression line equation is used to predict (or estimate) the value of the response variable from a given value of the explanatory variable.

In statistical modeling, regression analysis is a collection of statistical techniques for estimating the associations between a dependent variable and one or more independent variables.

a) $\bar{y}$=β₀+β₁x

Where,

β₁=$S_{xy}$/$S_{xx}$ -------(1)

Where,

$S_{xy}$= -341.959231

$S_{xx}$1585.230769

By substituting these values in equation 1 we get,

β₁= -0.2157

β₀= $\bar{y}$-β₁x

Where,

$\bar{y}$=∑$y_{i}$/n

∑$y_{i}$=52.8

n=13

Then,

$\bar{y}$=4.0615

$\bar{x}$=∑$x_{i}$/n

∑$x_{i}$=303.7

n=13

$\bar{x}$=23.3615

β₀=4.0615-(-0.2157)(23.3615)

=9.1006

Therefore, β₀=9.1006

The regression equation is  $\bar{y}$=9.1006+(-0.2157)x

If x=25,

$\bar{y}$=9.1006+(-0.2157)(25)

$\bar{y}$=3.7081

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