Question

Find data below which enumerates beers' various costs and critical scores.
Beer	Price	Score
A	5	56
B	10	48
C	15	65
D	18	60
E	20	80
F	25	70
G	30	61
H	12	68
Plot the data. Which field do you choose as your independent variable?
Use the data to make a linear regression equation. What is the coefficient of correlation?
Use the t-test to determine whether the variables are independent or not.

Answer 1

The plot is:

35 E 30 25 20 Price 15 10 5 0 H 40 50 60 70 80 90 Score

Critical scores is the independent variable.

The linear regression equation is:

y = 0.366 x - 6.353

R = 0.433

The hypothesis being tested is:

H₀: β₁ = 0

H₁: β₁ ≠ 0

The test statistic, t = 1.177

The p-value is 0.2836.

Since the p-value (0.2836) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the variables are independent.

	r²	0.188
	r	0.433
	Std. Error	7.933
	n	8
	k	1
	Dep. Var.	Price
ANOVA table
Source	SS	df	MS	F	p-value
Regression	87.2427	1	87.2427	1.39	.2836
Residual	377.6323	6	62.9387
Total	464.8750	7
Regression output				confidence interval
variables	coefficients	std. error	t (df=6)	p-value	95% lower	95% upper
Intercept	-6.3531
Score	0.3658	0.3107	1.177	.2836	-0.3944	1.1260