calculus help pleaseee :(

Question

GEorge pierce studied how temperature would affect the behavior of crickets . He thought that crickets would be less active at lower temperature,since they are a cold-blooded animal. The results of his study are shown in the table below. Use your calculator to create a scatterplot and complete a linear regression to create a line of best fit. Draw an accurate graph of the scatterplot and the line. then use your equation and/or the scatterplot to answer the questions. below is the CRICKET BEHAVIOR :

temp (ºC)	chirps/second
20.0	89
16.0	72
19.8	93
18.4	84
17.1	81
15.5	75
14.7	70
15.7	72
15.4	69
16.3	83
15.0	80
17.2	83
16.0	81
17.0	84
14.4	76

a) write your regression equation rounding all values to three decimal places.

b) show how you could use your equation to predict the number of chirps/second when the temperature is 25ºC.

c) Explain how you would use your graphing calculator to predict the temperature on a day when the crickets were chirping at a rate of 120 chirps/second.

d) If the temperature were drop to 0ºC, what would you expect the rate of chirping to be based on your regression equation? in real life would this be an accurate prediction? why or why not?

Answer 1

(a)

The temperature and Chirps/second data table is

SNO	Temperature °C X	Chirps/second Y	XY	X²	Y²
1	20.0	89	1780	400	7921
2	16	72	1152	256	5184
3	19.8	93	1841.4	392.04	8649
4	18.4	84	1545.6	338.56	7056
5	17.1	81	1385.1	292.41	6561
6	15.5	75	1162.5	240.25	5625
7	14.7	70	1029	216.09	4900
8	15.7	72	1130.4	246.49	5184
9	15.4	69	1062.6	237.16	4761
10	16.3	83	1352.9	265.69	6889
11	15.0	80	1200	225	6400
12	17.2	83	1427.6	295.84	6889
13	16.0	81	1296	256	6561
14	17.0	84	1428	289	7056
15	14.4	76	1094.4	207.36	5776
∑	∑X = 248.5	∑Y = 1192	∑XY = 19887.5	∑X² = 4157.89	∑Y² = 95412

We make use of Linear Regression.

A linear Regression is in the form of y = a + bx

Where y is the chirps/second and x is the Temperature.

The values of a and b is given by

The Linear Regression is y = 22.980 + 3.409x.

Graph the data table and the regression Equation.

Therefore the linear regression Equation is y = 22.980 + 3.409x.

Answer 2

(b)

The linear Regression Equation is y = 22.980 + 3.409x.

when the Temperature is 25°C,

Substitute x = 25 in the Linear Regression Equation.

y = 22.980 + 3.409*25

y = 108.205 chirps/second.

Therefore the number of  chirps/second is 108 when temperature is 25°C.

Answer 3

(c)

The linear Regression Equation is y = 22.980 + 3.409x.

Graph the data table and the Regression Equation.

From the Graph, we observe that when the crickets chirps at rate of 120 chirps/seconds, then the temperature is 28.45°C.

Answer 4

(d)

The linear Regression Equation is y = 22.980 + 3.409x.

when the temperature is 0°C,

Substitute x = 0 in the linear Regression, then y = 22.980.

This is linear regression equation is not suitable because the crickets would not chirp at 0°C of temperature.