Math Problem Statement

A scientist collected the following data on the speed, in centimeters per second, at which ants ran at the given ambient temperature, in degrees Celsius.† Temperature Speed 25.6 2.62 27.5 3.03 30.3 3.57 30.4 3.56 32.2 4.03 33.0 4.17 33.8 4.32 (a) Find the equation of the regression line, giving the speed S as a function of the temperature t. (Round the regression line parameters to four decimal places.) S(t) =

(b) Explain in practical terms the meaning of the slope of the regression line. (Round your answers to four decimal places.) The slope of means that for each increase in temperature of one degree Celsius, the ants run centimeters per second faster

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Statistics
Algebra

Formulas

S(t) = a + bt (equation of the regression line)
b = [nΣ(t*S) - ΣtΣS] / [nΣt^2 - (Σt)^2] (formula for the slope)
a = [ΣS - bΣt] / n (formula for the intercept)

Theorems

Least Squares Method

Suitable Grade Level

Grades 10-12