Public Health and Nutrition Research suggests that salt intake is related to fluid intake in adults and soft drink consumption in children and adolescents. Suppose a random sample of 18 children and adolescents was obtained and the amount of salt consumed (x, g/week) and the amount of sugar-sweetened soft drinks consumed (y, g/week) was recorded for each. The following summary statistics were obtained.
ΣXi = 430
ΣYi = 17,512
ΣXiyi = 441,608
ΣXi2 = 11,138
ΣYi2 = 18,197,768
a. Find the estimated regression line, and complete the ANOVA table.
b. Conduct an F test for a significant regression. Find bounds on the p value for this test.
c. Conduct the hypothesis test H0: β1 = 25 versus Ha: β1 ≠ 25. Use a significance level of 0.05.
d. Find a 99% confidence interval for the true value of b1.