Mr. And Mrs. Harper are planning to install a deck and a garden. Help them determine which of the two choices below is most effi
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Answer:
Residual = -2
The negative residual value indicates that the data point lies below the regression line.
Step-by-step explanation:
We are given a linear regression model that relates daily high temperature, in degrees Fahrenheit and number of lemonade cups sold.
Where y is the number of cups sold and x is the daily temperature in Fahrenheit.
Residual value:
A residual value basically shows the position of a data point with respect to the regression line.
A residual value of 0 is desired which means that the regression line best fits the data.
The Residual value is calculated by
Residual = Observed value - Predicted value
The predicted value of number of lemonade cups is obtained as
So the predicted value of number of lemonade cups is 23 and the observed value is 21 so the residual value is
Residual = Observed value - Predicted value
Residual = 21 - 23
Residual = -2
The negative residual value indicates that the data point lies below the regression line.
Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2 and a quadratic finction, say g(x), such that g(0) = 0 and g(1) = 1.
The rate of change of a function f(x) over an interval
is given by
Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval
is given by
Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval
is given by
Therefore, the exponential grows at the same rate as the quadratic in the interval <span>.</span>
The rate of change of a function f(x) over an interval
is given by
Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval
is given by
Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval
is given by
Therefore, the exponential grows at the same rate as the quadratic in the interval <span>