The following table shows the average price of a two-bedroom apartment in downtown New York City during the real estate boom from 1994 to 2004.† t 0 (1994) 2 4 6 8 10 (2004) Price ($ million) 0.38 0.40 0.60 0.95 1.20 1.60 (a) Use exponential regression to model the price P(t) as a function of time t since 1994. (Round the coefficients to 3 decimal places.)  P(t) =       Select a sketch of the points and the regression curve.       b) Extrapolate your model to estimate the cost of a two-bedroom downtown apartment in 2005. (Round your answer to one decimal place.)$  million

In the following time series linear regression equation, t is time in years and y is sales in millions of dollars: ýt = Interpret the regression coefficient. = 11. 602 + 3.46t For every one year increase in time, sales increase by $3.46 million on average. For every one year increase in time, sales decrease by $3.46 million on average. As time increases, sales fluctuate around a constant mean of $3.46 million. For every one year increase in time, sales decrease by $346 million on average.

Suppose that a simple linear regression model is appropriate for describing the relationship between y = house price (in dollars) and x = house size (in square feet) for houses in a large city. The population regression line is y = 22,500 + 43x and ?e = 4,000. b) Approximately what proportion of 2,000 sq ft homes would be priced over $110,000? (You may need to use a table. Round your answer to four decimal places.)   Approximately what proportion of 2,000 sq ft homes would be priced under $100,000? (You may need to use a table. Round your answer to four decimal places.)

Comment on the following statement: "The cost function for logistic regression trained with 100 examples is always non- negative."

2

The average top ticket price for Broadway musicals has increased dramatically between 1975 and 2003. 1985 1998 2000 2003 72.83 118.97 130.15 44.99 Year Average Ticket Price 1975 13.63 a. Using the data in the table, find the linear regression equation that best fits the data. (Let x = 0 represent the number of years since 1970.) y = (Round values to three decimal places.) b. Predict the average top ticket price for Broadway musicals in the year 2012 if the price continues to increase at the same rate. (Let x represent the number of years since 1970.) (Round to two decimal places.) c. Find the rate at which the price is rising. per year (Round to two decimal places.)