Question

The following data were taken from a study relating the Days High Temperature to the Average Amount of Cola Consumed (per capita) in a small mid-western town.

Observation Days High Temperature Average Ounces of Cola Consumed
1 64 73
2 51 61
3 62 55
4 78 75
5 50 53
6 80 81
7 50 53
8 52 54
9 61 77
10 69 82

Given the 10 Observations above, Use a Regression to find each of the following:

a. Slope of Regression Equation =
b. Y Intercept for the Regression Equation =
c. Correlation Coefficient =
d. Coefficient of Determination =

Answer 1

a. Slope of Regression Equation = 0.89064

b. Y Intercept for the Regression Equation = 11.44751

c. Correlation Coefficient = 0.8167

d. Coefficient of Determination = 0.667

Explanation:

Given the data:

High temperature (X) :

64

51

62

78

50

80

50

52

61

69

Ounces of cola consumed (Y) :

73

61

55

75

53

81

53

54

77

82

Using a Regression calculator :

The regression equation obtained is :

ŷ = 0.89064X + 11.44751

Where ;

m = 0.89064 ; intercept, c = 11.44751

Correlation Coefficient measures the degree of relationship or association between an independent and dependent variable. The correlation Coefficient is 0.8167.

The Coefficient of determination, R² ; 0.8167² = 0.667