Question

1. The ministry of Health wishes to determine if there is a relationship between the number of cigarettes smoked daily and life time health care costs The result of six sample smokers is recorded below.

Number of Cigarettes	Health Costs (in thousands$)
30	43
40	45
50	54
60	53
70	56
80	63

1. Calculate the correlation coefficient
2. Test is the correlation coefficient is different from zero (.01 level)
3. Create the Ordinary Least Squares regression line
4. Discuss the assumptions that you make in order to use the OLS line as a predictor.

Answer 1

1. Calculate the correlation coefficient

The correlation coefficient is 0.958.

1. Test is the correlation coefficient is different from zero (.01 level)

The hypothesis being tested is:

H0: ρ = 0

Ha: ρ ≠ 0

The t-statistic is 6.664.

The p-value is 0.0026.

Since the p-value (0.0026) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the correlation coefficient is different from zero.

1. Create the Ordinary Least Squares regression line

The Ordinary Least Squares regression line is:

y = 31.5905 + 0.3771*x

1. Discuss the assumptions that you make in order to use the OLS line as a predictor.

There are four assumptions associated with a linear regression model:

1. Linearity: The relationship between X and the mean of Y is linear.
2. Homoscedasticity: The variance of residual is the same for any value of X.
3. Independence: Observations are independent of each other.
4. Normality: For any fixed value of X, Y is normally distributed.

Number of Cigarettes	Health Costs (in thousands$)
30	43
40	45
50	54
60	53
70	56
80	63
	r²	0.917
	r	0.958
	Std. Error	2.367
	n	6
	k	1
	Dep. Var.	Health Costs (in thousands$)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	248.914	1	248.9143	44.41	.0026
Residual	22.4190	4	5.6048
Total	271.333	5
Regression output				confidence interval
variables	coefficients	std. error	t (df=4)	p-value	95% lower	95% upper
Intercept	31.5905
Number of Cigarettes	0.3771	0.0566	6.664	.0026	0.2200	0.5343

Please give me a thumbs-up if this helps you out. Thank you!