can someone answer these 1 Over the past 50 years there has

can someone answer these:

1. Over the past 50 years, there has been a strong negative correlation between average annual income and the record time to run 1 mile. In other words, average annual incomes have been rising while the record time to run 1 mile has been decreasing. Do you think increasing incomes causes decreasing times to run the mile? Explain. What lurking variables might be causing the increase in one or both of the variables? Explain.

2. You conducted a study and found that the correlation between the price of a gallon of gasoline and gasoline consumption has a linear correlation coefficient of –0.7. What does this result say about the relationship between price of gasoline and consumption? If the study included gasoline prices ranging from $2.70 to $5.30 per gallon, is it reliable to apply the results of this study to prices of gasoline higher than $5.30 per gallon? Explain.

3. When we use a least-squares line to predict y values for x values beyond the range of xvalues found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?

Solution

2.The correlation between the price of a gallon of gasoline and gasoline consumption has a linear correlation coefficient of –0.7. Thus, it may be said that there is a negative correlation between the two variables. That is when one variable increases the value of the other variable decreases.

3.When one is using least-squares line to predict y values for x values beyond the range of x values found in the data then we are extrapolating.