Hi, can someone help me with these questions please?

1) 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 2013 Fuel Economy Guide give the regression line

highway mpg = 6.785 + (1.033 city mpg)

for predicting highway mileage from city mileage.

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

1.2) What is the intercept? (Enter your answer to three decimal places.)

1.3) Find the predicted highway mileage for a car that gets 14 miles per gallon in the city. (Round your answer to two decimal places.)

1.4) Find the predicted highway mileage for a car that gets 25 miles per gallon in the city. (Round your answer to two decimal places.)

2) 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. Here are the data:

Sea Surface Temperature 29.67 29.88 30.17 30.22 30.49 30.66 30.90

Growth 2.63 2.58 2.68 2.70 2.48 2.39 2.26

2.1) Find the mean and standard deviation of both sea surface temperature x and growth y and the correlation r between x and y. Use these basic measures to find the equation of the least-squares line for predicting y from x. (Round your answers to three decimal places.)

= ____ + ____x

2.2) 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.

3) We found some measurement error in our recordings of sea surface temperature and coral growth. The new data values are below, and the equation predicting coral growth y from mean sea surface temperature x is = 11.6921 0.30305x.

Sea Surface Temperature 29.68 29.87 30.16 30.22 30.48 30.65 30.90

Growth 2.63 2.58 2.68 2.60 2.48 2.38 2.26

3.1) Use the above least squares equation to obtain the seven residuals step by step. That is, find the prediction for each x value of mean sea surface temperature, and then find the residual y . (Round your answers to three decimal places.)

y -

3.2) Find the sum of the residuals (up to roundoff error). (Round your answer to 3 decimal places.)

3.3) The residuals are the part of the response y left over after the straight-line tie between y and x is removed. Find the correlation between the residuals and x values. (Round your answer to 3 decimal places.)

6) A newspaper advertisement contained pictures of diamond rings with gold bands and listed their prices and diamond weight (in carats). The least squares regression line for predicting price (in dollars) from the weight of the diamond (in carats) is the following.

Price = 254.65 + 3725.09 Carats

6.1) What does the slope of this line say about the relationship between price and number of carats? (Enter your answer to the nearest cent.)

Increasing the size of a diamond by 1 carat increases its price by ? on average?

6.2) What is the predicted price when number of carats = 0? (Enter your answer to the nearest cent.)