14.30 Guess the correlation. For each of the following pairs of variables, would you expect a substantial negative correlation, a substantial positive correlation, or a weak correlation? a. The cost of a cable TV service and the number of channels provided by the service. b. The weight of a road-racing bicycle and the cost of the bicycle. c. The number of hours a student spends on Facebook and the student's GPA. d. The heights and salaries of faculty members at your university.

Assume the correlation coefficient between advertising dollars spent and sales is .78. How much of the variability in sales is explained by the relationship between sales and advertising dollars? a. 39.16% b. 60.84% c. 78% d. 22%

An economist wants to determine whether there is a linear relationship between a country's gross domestic product (GDP) and carbon dioxide emissions. The data are shown in the table below. c. Compute and interpret the correlation coefficient. d. Compute and interpret the coefficient of determination. e. Test for the significance of the linear relationship. Use a 0.05 level of significance. State your conclusion. Hint: Your conclusion is either of the following. • There is a significant linear relationship between a country's gross domestic product (GDP) and carbon dioxide emissions. • There is no significant linear relationship between a country's gross domestic product (GDP) and carbon dioxide emissions. GDP 1.6 3.6 4.9 1.1 0.9 2.9 2.7 2.3 1.6 1.5 (trillion dollars) Carbon Dioxide Emissions 428.2 828.8 1214.2 444.6 264 415.3 571.8 454.9 358.7 573.5 (millions of metric tons)

Which of the following correlations indicates the strongest relationship or association and why? r = .10; r = .03; r = -.35; r = -15

Dr. Erie, a researcher at the Moore County Botany Institute, reported the following correlations. The correlation between pH level of soil and tomato weight is r₁ = -0.4. The correlation between hours of sunlight and tomato weight is r2 = 0.1. According to this information, which of the following statements are true? Select all that apply. Larger tomatoes result from more daily hours of sunlight. Larger tomatoes result from higher soil pH level. Tomato size is related more strongly to hours of sunlight than to soil pH level. None of these are true.