stats chapter 3

Suppose we fit the least-squares regression line to a set of data. Ifa plot of the residuals shows a curved pattern,

a straight line is not a good summary for the data.

Below is a scatter plot (with the least squares regression line) for calories and protein (in grams) in one cup of 11 varieties of dried beans. The computer output for this regression is below the plot. Yuse scenario 3 - 7. The circled point on the scatter plot represents lima beans, which have 621 calories and 37 grams of protein. The residual for lima beans is

- 4.18

Scenario 3-1 The height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. The goal is to determine if volume of usable lumber can be estimated from the height of a tree. Use Scenario 3-1. Which of the following statements are supported by the scatterplot? 1. There is a positive association between height and volume. 2. There is an outlier in the plot. 3. As the height of a cherry tree increases, the volume of useable lumber it vields increases

1., 2., and 3.

Consider the following scatter plot of amounts of CO ( carbon monoxide) and NOX(nitrogen oxide) in grams per mile driven in the exhaust of cars. The least- squares regression line has been drawn in the plot. Based on the scatter plot, the least- squares line would predict that a car that emits 10 grams of CO per mile driven would emit approximately how many grams of NOX per mile driven

1.1.

Consider the following scatter plot of amounts of CO ( carbon monoxide) and NOX(nitrogen oxide) in grams per mile driven in the exhaust of cars. The least- squares regression line has been drawn in the plot. The intercept of the least-squares regression line is approximately

1.8.

In a statistics course a linear regression equation was computed to predict the final exam score from the score on the first test. The equation of the least-squares regression line was ŷ=10+0.9x. Where y represents the predicted final exam score and x is the score on the first exam. Suppose Joe scores a 90 on the first exam. What would be the predicted value of his score on the final exam?

91

Scenario 3-9 A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so r helps explain y. The least-squares regression line for predicting y from x is ŷ=1344- 19x You scenario 3-9. On a day when the temperature is 20ﾟF, the regression line predicts that gas used will be about

946 ft³

Which of the following statements describes what the standard deviation of residuals for regression equation can be used for? 1. It describes the typical verticle distance between the observed data point and the regression line. 2. It evaluates whether linear model is appropriate forset of data. 3. It measures the overall precision of predictions made using the regression equation.

Both 1 and 3

Consider the following scatter plot, which describes the relationship between stopping distance (in feet) and air temperature (in degrees Centigrade) for a certain 2,000-pound car travelling 40 mph. if another data point were added with an air temperature of 0° C and a stopping distance of 80 feet, the correlation would

Decrease, since this new point is an outlier that does not follow the pattern in the data

Below is a scatter plot (with the least squares regression line) for calories and protein (in grams) in one cup of 11 varieties of dried beans. The computer output for this regression is below the plot. Use Scenario 3-7. Which of the following statements is a correct interpretation of the slope of the regression line?

For each 1-unit increase in the calorie content, the predicted protein content increases by 2.08 g.

Which one of the following statements is correct?

If people with larger heads tend to be more intelligent, then we would expect the correlation between head size and intelligence to be positive.

There is a positive correlation between the size of a hospital (measured by number of beds) and the median number of days that patients remain in the hospital. Does this mean that you can shorten a hospital stay by choosing to go to a small hospital?

No - the positive correlation is probably explained by the fact that seriously ill people go to large hospitals.

Scenario 3-9 A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so r helps explain y. The least-squares regression line for predicting y from x is ŷ=1344- 19x Use Scenario 3-9. What does the number 1344 represent in the equation?

Predicted gas usage (in cubic feet) when the temperature is 0ﾟF

The least-squares regression line is fit to a set of data. If one of the data points has a positive residual, then the correlation between the values of the response and explanatory variables must be positive.

The point must lie above the least-squares regression line.

Below is a scatter plot (with the least squares regression line) for calories and protein (in grams) in one cup of 11 varieties of dried beans. The computer output for this regression is below the plot. Use Scenario 3-7. Which of the following best describes what the number S = 3.37648 represents?

The standard deviation of the residual is 3.37648.

Suppose a straight line is fit to data having response variable y and explanatory variable x. Predicting values of y for values of x outside the range of the observed data is called

extrapolation

Consider the following scatter plot of amounts of CO ( carbon monoxide) and NOX(nitrogen oxide) in grams per mile driven in the exhaust of cars. The least- squares regression line has been drawn in the plot. In the scatter plot, the point indicates by the open circle

has a negative value for the residual.

If removing an observation from a data set would have a marked change on the equation of the least-squares regression line, the point is called

influential

Consider the following scatter plot, which describes the relationship between stopping distance (in feet) and air temperature (in degrees Centigrade) for a certain 2,000-pound car travelling 40 mph. the correlation between temperature and stopping distance

is approximately 0.6.

Consider the following scatter plot of two variables X and Y. We may conclude that the correlation between X and Y

is close to 1, even though the relationship is not linear.

Scenario 3-9 A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so r helps explain y. The least-squares regression line for predicting y from x is ŷ=1344- 19x You scenario 3 - 9. When the temperature goes up 1 degree, what happens to the gas usage predicted by the regression line?

it goes down 19 ft³

Two variables are said to be negatively associated if

larger values of one variable are associated with smaller values of the other.

"Least-squares" in the term "least-squares regression line" refers to

minimizing the sum of the squares of the residuals.

Scenario 3-1 The height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. The goal is to determine if volume of usable lumber can be estimated from the height of a tree. Use Scenario 3-1. If the data point (65,70) were removed from this study, how would the value of the correlation r change?

r would be larger, since this point does not fall in the pattern of the rest of the data.

You would draw a scatter plot to

show the relationship between the height of female students and the heights of their mothers

In a statistics course a linear regression equation was computed to predict the final exam score from the score on the first test. The equation of the least-squares regression line wasŷ=10+0.9x where y represents the predicted final exam score and x is the score on the first exam. The first test score is

the explanatory variable.

which of the following are most likely to be negatively correlated

the prices and weights of all racing bicycles sold last year in Chicago.

correlation coefficient measures

the strength of the linear relationship between two quantitative variables.

Scenario 3-1 The height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. The goal is to determine if volume of usable lumber can be estimated from the height of a tree. Use Scenario 3-1. In this study, the response variable is

volume of lumber

A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil. The response variable in this study is

yield to the crop