Question

9. The caloric contents and the sodium contents (in milligrams) of 10 beef hot dogs is given below. (Source: Consumer Reports)

Calories x	150	170	120	120	90	180	170	140	90	110
Sodium y	420	470	350	360	270	550	530	460	380	330

1. Find the equation of the regression line.

Y = 80.819 +2.4715x

2. Slope of the regression line you wrote in part A = 2.4715 Write a sentence to interpret this value in the context of the problem

3. Calculate the correlation coefficient, r. Write a sentence to interpret this value in the context of the problem r = ______

                        Correlation of r is 0.9064

4. Calculate the coefficient of determination, . Interpret this value in the context of the problem.

______ 0.

                                                Calculated r^2 = 0.822

5. Use the regression equation (in part A) to predict the value of sodium content (in milligrams) for a beef hot dog that has 130 calories.

6. Using , conduct a t - test for significance to determine if there is a significant relationship between the caloric content and the sodium content of beef hot dogs.

Answer 1

Ru regression analysis in excel

Regression equation: y = 2.4715x + 80.813

Slope of the regression line you wrote in part A = 2.4715

Calculate the correlation coefficient, r. = 0.9064

Calculate the coefficient of determination, .= 0.822

formula =0.9062^2 = 0.822

Use the regression equation (in part A) to predict the value of sodium content (in milligrams) for a beef hot dog that has 130 calories.

x = 130

y = 2.4715x + 80.813

y = 2.4715*130+ 80.813

y = 402 (rounded to whole number)

so the predicted value of 130 calories is 402

Using , conduct a t - test for significance to determine if there is a significant relationship between the caloric content and the sodium content of beef hot dogs.

Run t-Test: Two-Sample Assuming Equal Variances in excel

P-value = 0.00000003 lesser than the significance level 0.05

The p-value less than 0.05 (typically ≤ 0.05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct . so there is a significant relationship between the caloric content and the sodium content of beef hot dogs