Question

recorded temperatures (in F) and precipitation in (inches) at a place are as follows: Temperature(x) 86, 81,83,89,90,74,64 Precipitation(y) 3.4,1.8,3.5,3.6,3.7,1.5,0.2 A Find the sample correlation coeficcient, r B. What is the meaning of the value of r that you have calculated in part A? C. Find the significance of the population correlation coefficient, p at a=0.05 D. Find the value of the coefficient of variation r2 E. What is the meaning of r2 value you have calculated in part D? F. Find y, when x=70 G. Find the standard error of the estimate Has to be done in excell

Answer 1

a)

Computational Table:

	X	Y	X2	Y2	XY
	86	3.4	7396	11.56	292.4
	81	1.8	6561	3.24	145.8
	83	3.5	6889	12.25	290.5
	89	3.6	7921	12.96	320.4
	90	3.7	8100	13.69	333
	74	1.5	5476	2.25	111
	64	0.2	4096	0.04	12.8
Total	567	17.7	46439	55.99	1505.9

A) Find Correlation Coefficient (r):

r = 0.95

B)

There is High degree of Positive correlation coefficient between Temperature(X) & Precipitation (Y)

C)

Hypothesis:

(No linear correlation)

(Positive linear correlation)

Test statistic:

Degrees of freedom = n-2 = 7-2 = 5

P-value: 0.0009 .............From t table

Conclusion:

p-value < , i.e 0.0009 < 0.05, That is Reject Ho at 5% level of significance.

Therefore, population correlation coefficient statistically significant at the 5% level of significance.

D)

Coefficient of Determination (R²) = r² = 0.95² = 0.9063

E)

This result means that 95% of the variation in the dependent variable is accounted for by the variation in the independent variable. The rest of the variation, 0.05, or 5% is unexplained. This value is called the coefficient of non-determination and is found by subtracting the coefficient of determination from 1.

F)

For slope:

b = 0.14

For Intercept:

a = -8.89

Therefore, the least square regression line would be,

Find Y when X = 70

Therefore, above equation becomes........

G)