Question

45. Although many people buy fast food because it is cheap, quick and heavily advertised, these meals can contain large amount of sodium or salt. Some researchers suggest that the amount of sodium is linearly related to total calories. A sample of Burger King’s sandwiches was obtained, and the total calories (x) and sodium (y, in grams) for some serving was measured. (The data is given in the table at the end).

a) Draw a scatter diagram and identify any outlier.

b) Obtain the regression equation and plot it on the scatter diagram

c) Compute the coefficient of determination and interprete its meaning in the context of the problem.

d) Construct an ANOVA table

e) Use the t statistics to test the hypothesis of a positive linear relationship. Let = 0.05.

f) Determine the p-value for the hypothesis test in part (e).

g) State your conclusion in terms of the problem

h) Construct the 95% confidence interval for the slope of the regression.

i) Compute the sample Pearson's correlation coefficient.

j) Test for the existence of a direct correlation and state your conclusion. Use = 0.05.

Table 3 – Problem 45

Calories Sodium

220	490
310	670
260	700
960	2010
440	1300
330	680
320	860
260	690
360	810
430	870
830	1880
430	1120
310	630
320	960
330	730
220	490
700	1440
320	950
540	1360
260	760

Answer 1

a)

b) regression equation is Y = 147.72 + 2.02 X

This regression equation is shown on the scatter plot above.

c) coefficient of determination.

This means that 91.73% of the variation in Y can be explained by X.

e - g)

Since the null hypothesis is rejected we have evidence that there is a significant relationship between the two variable.