Statistics homework help

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STAT 200 Week 7 Homework Problems
10.1.1
Does education pay? The scatter diagram drawn in MiniTab shows the relation between the percentage of the population of a state plus Washington, DC, that has at least a bachelor’s degree and the median income (in dollars) of the state for 2013. Source: U.S. Census Bureau
 
 
 
 
 
Describe any relation that appears to exist between the level of education and median income.
One observation appears to stick out from the rest. Which one? This particular observation is for Washington, DC. Can you think of any reasons why DC, outlies the other states?
The correlation coefficient between the percentage of the population with a bachelor’s degree and median income is 0.854. Does a linear relation exist between percent of the population with at least a bachelor’s degree and median income?
10.1.2
Education and Birthrate. The following scatter diagram drawn in Excel shows the relation between the percent of the population with at least a bachelors degree in a state and birthrate (births per 1000 women 15 to 44 years old).
 
 
 
 
 
Describe any relation that exists between median income and birthrate.
The correlation between percent of population with at least a bachelor’s degree and birth rate is -0.069. What does this imply about the relation between median income and birthrate?
10.1.3
In Problem 10.1.1, a scatter diagram and correlation coefficient suggested there is a linear relationship between the percentage of individuals who have at least a bachelor’s degree and median income in the states. In fact, the least-squares regression equation is where y is the median income and x is the percentage of individuals 25 years and older with at least a bachelor’s degree in the state.
Predict the median income of a state in which 25% of adults 25 years and older have at least a bachelor’s degree.
In North Dakota, 27.1 percent of adults have at least a bachelor’s degree. The median income in North Dakota is $37,193. Is this income higher than what you would expect? Why?
Interpret the slope.
Explain why it does not make sense to interpret the intercept.
10.1.4
Table #1 contains the value of the house and the amount of rental income in a year that the house brings in (“Capital and rental,” 2013). Create a scatter plot and find a regression equation between house value and rental income. Then use the regression equation to find the rental income a house worth $230,000 and for a house worth $400,000. Which rental income that you calculated do you think is closer to the true rental income? Why?
Table #1: Data of House Value versus Rental
 
 
10.1.5
An engineer wants to determine how the weight of a car, x, affects gas milage, y. The following data represents the weights of various domestic cars and their miles per gallon in the city for the 2018 model year.
 
 
 
 
 
Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.
Interpret the slope and y-intercept, if appropriate.
A Cadillac CTS weighs 3649 pounds and gets 20 miles per gallon. Is the miles per gallon of a CTS above average or below average for this weight?
Would it be reasonable to use the least-squares regression line to predict the miles per gallon of a Toyota Prius, a hybrid gas and electric car? Why or why not?