Question

Altitude and Temperature: listed below are altitudes (thousands of feet) and outside air temperature (degress fehrenheit) recorded by the author during delta flight 1053 from New Orleans to Atlanta. Altitude(x): 3 10 14 22 28 31 33 Tempertaure(y): 57 37 24 -5 -30 -41 -54

A. Draw scatter plot for the variables

B. Compute the value of the correlation coefficient

C. State the hypotheses

D. Test the significance of the correlation coefficient at alpha = 0.05 using table 1

E. Give a breif explination of the type of relationship

F. Find the equation of the regression line

G. Graph the equation of the regression line on your scatter plot.

H. If the altitude is 7 (thousand feet) estimate the temperature using the regression euation

Answer 1

Ans:

Scatter plot:

	x	y	xy	x^2	y^2
1	3	57	171	9	3249
2	10	37	370	100	1369
3	14	24	336	196	576
4	22	-5	-110	484	25
5	28	-30	-840	784	900
6	31	-41	-1271	961	1681
7	33	-54	-1782	1089	2916
Total	141	-12	-3126	3623	10716

r=(7*-3126-141*-12)/SQRT((7*3623-141^2)*(7*10716-(-12)^2))=-0.997

n=7

df=7-2=5

critical r value=0.754

As,absolute value of sample correlation cofficient i.e. 0.997 is greater than critical value,we reject the null hypothesis and we can conclude that there is a significant correlation between Altitude and temperature.

There is strong negative correlation between Altitude and temperature i.e. as the altitude increases,temprature tends to decrease.

	x	y
mean=	20.14	-1.71
std. dev.=	11.423	42.221
r=	-0.997
slope,b=	-3.684
intercept,a=	72.50

Regression eqn:

y'=-3.684x+72.50

When x=7

y'=-3.684*7+72.50=46.7