helo I have 14 statistics questions

1.

(a) Find the linear correlation coefficient r.  
(b) Determine whether there is a linear correlation between the two variables?.

2. Listed below are the chest sizes (in inches) and weights (in pounds) of randomly selected bears that were anesthetized and measured. Because it is much more difficult to weigh a bear than to measure its chest size, the presence of a correlation could lead to a method for estimating weight based on chest size.

(a) Find the linear correlation coefficient r.  

3. IQ scores were obtained from randomly selected twins separated at birth. For 20 such twins, the linear correlation coefficient is 0.816 and the equation of the regression line is  = -2.97 + 1.21x, where x represents the IQ score of the twin that was first-born. Also, the 20 x values have a mean of 106.6 and the 20 y values have a mean of 100.6. What is the best predicted IQ of a twin who was born second, given that the first-born twin has an IQ of 113? 

4. The author collected data from 16 cereals consisting of the sugar contents (in grams per gram of cereal) and the calories (per gram of cereal). Excel was used to find that the linear correlation coefficient is r = 0.703 and the equation of the regression line is  = 3.13 + 1.05x, where x represents the sugar content. Also, the mean calorie amount is 3.12 calories per gram of cereal. What is the best predicted calorie content for a cereal with a 0.31 gram of sugar per gram of cereal? 

5. Find the regression equation (rounding values to 2 places), letting the first variable be the independent variable x. 
Use the regression equation values to find the best predicted gross amount for a movie with a budget of 77 million dollars. Hint: Use the exact regression values to find an accurate predicted value and then round your answer. 
In the table below, all amounts are in millions of dollars.

6. Find the regression equation, letting the first variable be the independent variable x. 
Round to 3 places if necessary.

7. Find the explained variation, unexplained variation, total variation, coefficient of determination, and standard error of estimate. Round to a minimum of 4 decimal places, if necessary. 
Eight different second-year medical students took blood pressure measurements of the same patient and the results are listed below.

 Explained variation
 Unexplained variation
 Total variation
 r2
 se

8. In each of the following cases, find the best predicted value for y given that x = 3.00. The given statistics are summarized from paired sample data. Use the given data to find the best predicted value of the dependent variable. Be sure to follow the prediction procedures.

(a) r = 0.987, y = 6.00, n = 20, and the equation of the regression line is  = 7.00 + 4.00x.
 
(b) r = 0.059, y = 6.00, n = 20, and the equation of the regression line is  = 7.00 + 4.00x.

9. Consider the following:

(a) Suppose you are given the following x, y data pairs.

Find the least-squares equation for these data. (Use 3 decimal places.)

(b) Now suppose you are given these x, y data pairs.

Find the least-squares equation for these data. (Use 3 decimal places.)

(d) Solve your answer from part (a) for x. (Use 3 decimal places.)

10. Compute the sample correlation coefficient r for each of the following data sets. (Use 3 decimal places.) 

11. Refer to the set of data values for Diamonds (posted above within the instructions under Additional Resources). 

(a) Use the paired data consisting of the carat weight (x) and the price (y). What is the best predicted price of a diamond with a weight of 1.5 carats?
$  
(b) Use the paired color (x) and the price (y) data. What is the best predicted price of a diamond with a color rating of 8?
$  

12. We expect a car's highway gas mileage to be related to its city gas mileage (in miles per gallon, mpg). Data for all 1137 vehicles in the government's Fuel Economy Guide give the regression line

highway mpg = 6.785 + (1.033 * city mpg)

for predicting highway mileage from city mileage.

(a) What is the slope of this line? (Enter your answer to three decimal places.) 
  mpg 

(b) What is the intercept? (Enter your answer to three decimal places.) 
  mpg 
(c) Assume a strong linear correlation. Find the predicted highway mileage for a car that gets 17 miles per gallon in the city. (Round your answer to two decimal places.) 
  mpg 
Find the predicted highway mileage for a car that gets 21 miles per gallon in the city. (Round your answer to two decimal places.) 
  mpg 

13. Scientists measured the annual forest loss (in square kilometers) in a country from 2000 to 2012. They found the regression line

forest loss = 7600 + (1027 * year since 2000)

for predicting forest loss in square kilometers from years since 2000.

(c) If we measured forest loss in square meters per year, what would the slope be? Note that there are 106 square meters in a square kilometer. 
 m2 

(d) If we measured forest loss in thousands of square kilometers per year, what would the slope be? (Enter your answer to three decimal places.) 
 thousands of km2

14. A study is given in which scientists examined data on mean sea surface temperatures (in degrees Celsius) and mean coral growth (in millimeters per year) over a several-year period at different locations. (Sea surface temperature is x and growth is y.)

(a) Find the regression equation. (Round your answers to three decimal places.)
ŷ =  +  x
(b) Say in words what the numerical value of the slope tells you. (Round your answer to three decimal places.)

Every increase of one degree Celsius means about  fewer mean millimeters of coral growth per year.

14. The equation of a regression line, unlike the correlation, depends on the units we use to measure the explanatory and response variables. Here is the data on percent body fat and preferred amount of salt.

In calculating the preferred amount of salt, the weight of the salt was in milligrams.

(a) Find the equation of the regression line for predicting percent body fat from preferred amount of salt when weight is in milligrams. (Round your answers to one decimal place.) 

ŷ =  +  x

 
(b) A mad scientist decides to measure weight in tenths of milligrams. The same data in these units are as follows.

Find the equation of the regression line for predicting percent body fat from preferred amount of salt when weight is in tenths of milligrams. (Round your intercept to one decimal place and your slope to two decimal places.) 

ŷ =  +  x

 
(c) Use both lines to predict the percent body fat from preferred amount of salt for a child with preferred amount of salt 1 when weight is measured in milligrams, which is the same as 10 when weight is in tenths of milligrams. (Round your answers to one decimal place.)