Question

You will need your ticker code for stock prices for this question. Use your ticker code to obtain the closing prices for the following time period:

March 2, 2019 to March 16, 2019

Use the last two digits (the decimals) of the closing price and use them to replace the X.Xs in the following table. Notice that in the dataset a decimal point will separate the two digits. (already been done in the table)

Head Width (cm)	Bitting Force (grams/centimer^2)
4.31	129.5
3.92	115.8
2.56	92.7
3.72	106.1
4.21	123.6
2.95	106.8
4.74	130.5
2.84	111.0

Imagine that you are examining the functional relationship between head width (measured in centimeters) and biting force (measured in grams per square centimeters) in the tegu lizard.

a) Conduct a linear regression by hand. You will need to show the slope and the intercept of the best-fit line. Also, construct a scatterplot graph with all data-points and trace the best-fit line (if you want you can do the graph in Excel)

b) Conduct a hypothesis test for the significance of the slope of the best fit line (ANOVA table).

c) Calculate a 95% confidence interval on the slope. d) Calculate the coefficient of determination (r2).

Show your work and all calculations and explain all results!

Answer 1

Part (a)

x = Head Width(cm)

y = Bitting Force (gms/cm^2)

	x	y	x^2	y^2	xy
1	4.31	129.5	18.5761	16770.2500	558.145
2	3.92	115.8	15.3664	13409.6400	453.936
3	2.56	92.7	6.5536	8593.2900	237.312
4	3.72	106.1	13.8384	11257.2100	394.692
5	4.21	123.6	17.7241	15276.9600	520.356
6	2.95	106.8	8.7025	11406.2400	315.060
7	4.74	130.5	22.4676	17030.2500	618.570
8	2.84	111	8.0656	12321.0000	315.240
sum	29.25	916	111.2943	106064.84	3413.311

The regression equation is

The estimates of and are

The fitted regression equation is

Slope = 14.759

Intercept = 60.538

Part (b)

Correlation coefficient =r

Total Sum of Squares

Regression Sum of Squares

Residual SS

Total df = n-1 = 8-1=7

Reg df = 1

Resid df = n-2=8-2=6

Critical value of F with df 1 and 6 at 5% level = 5.9874

Source	SS	DF	MS	F	Critical
Regression	947.31	1	947.31	24.132	5.9874
Residuals	235.53	6	39.25
Total	1182.84	7

Since the computed value of F is more than the critical vaue, the regression coefficient is significant.

Part (c)

95% confidence interval for is

Part (d)