Question

In: Statistics and Probability

The caloric contents and the sodium contents (in milligrams) of 10 beef hot dogs is given...

  1. 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

  1. 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

  1. 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

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

______ 0.

                                                Calculated r^2 = 0.822

  1. 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.

  1. 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.

Solutions

Expert Solution

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

orchestra answered 1 year ago
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