problemsheet_6

# Problemsheet_6 - Regression Q1 A financial analyst wants to know the relationship between the return on Dalton Companys stock(Y and the overall

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Regression Q1 A financial analyst wants to know the relationship between the return on Dalton Company’s stock (Y) and the overall market return (X). He collects the following annual data for both variables: Y(%) 11 14 3 17 10 12 6 7 14 13 X(%) 10 12 8 15 9 11 8 10 13 11 = = = , 1222 , 1189 , 1309 2 2 xy x y (a) Find the least squares prediction line for these data. Interpret the slope coefficient of this model (i.e., explain what the number means, in the context of this particular problem). (b) The slope coefficient of this model is called the stock’s beta by investment analysts. A coefficient greater than 1 means that the stock is sensitive to changes in the overall market. Test the null hypothesis that Dalton Company’s stock is insensitive to the market against the alternative hypothesis that it is sensitive. Use α = .05. (c) Market analysts expect overall market return to be 10.5% next year. Find a 90% prediction interval estimate of the return on Dalton Company’s stock for next year under the assumption that the overall market forecast is accurate. (d) What percentage of the total variance in Dalton Company’s stock return is explained by this model? (e) What is a 98% confidence interval estimate of the average return on Dalton Company stock when the annual market return is 14%? Q2 Consumer Report magazine conducted a study to find out if cheaper brands of hot-dogs have a higher calorie content than the more expensive ones. They take a sample of 9 different brands of beef hot-dogs and measure the variables Y = ”Calorie content” and X = ”Price per ounce”. The data and part of the analysis is shown in the following tables. B r a n d s P r i c e C a l o r i e s Spike’s Beef 0.15 149 Hungry Hugh’s Jumbo Beef 0.10 184 Great Dinner Beef 0.11 190 RJB Kosher Beef 0.21 158 Wonder Kosher Skinless Beef 0.20 139

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Happy Fats Jumbo Beef 0.14 175 Midwest Beef 0.14 148 General Kosher Beef 0.23 152 Wall’s Kosher Beef Low Fat 0.25 111 Predictors Coef Stdev t-Ratio p Constant 218.2 17.95 Price 364.6 101.2 Notice that some of the numbers in the output are missing. (a) Interpret the slope coefficient in the context of this particular problem. (b) It is assumed that the price is not necessarily a good predictor of the calorie content. Perform a hypothesis test to verify this assumption. (c) Calculate the R-square and interpret the result. Q3 It is known that GMAT scores can be improved by training for the test. The following table gives increase in GMAT scores by four students after X hours of training. Hours of training 10 20 40 80 Average improvement 10 18 35 50 (a) Find the intercept and slope of the regression line by least squares. (b) Estimate the average improvement after 50 hours of training. (c) Find a 95% prediction interval for the score improvement after 30 hours of training. Q4 A university administered a newly designed entrance test to 25 students randomly selected from the new freshman class of a school in a study to determine whether a student’s grade point average (Y ) at the end of the freshman year can be predicted from this entrance test score (X). In the data set, X ranges from 3.5 to 7.8 and Y ranges from 1.6 to 4.7. The summary statistics are:
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## This note was uploaded on 09/18/2010 for the course BBA ISOM111 taught by Professor Hu during the Fall '08 term at HKUST.

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Problemsheet_6 - Regression Q1 A financial analyst wants to know the relationship between the return on Dalton Companys stock(Y and the overall

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