Exam 10: Inference for Regression

A random sample of 79 companies from the Forbes 500 list (which actually consists of nearly 800 companies)was selected,and the relationship between sales (in hundreds of thousands of dollars)and profits (in hundreds of thousands of dollars)was investigated by regression.The following results were obtained from statistical software. Suppose the researchers conducting this study wish to estimate the profits (in hundreds of thousands of dollars)for companies that had sales (in hundreds of thousands of dollars)of 500.The following results were obtained from statistical software. If the researchers wish to estimate the mean profits for all companies that had sales of 500,what would be a 95% confidence interval for the mean profits?

Do heavier cars use more gasoline? To answer this question,a researcher randomly selected 15 cars.He collected their weight (in hundreds of pounds)and the mileage (MPG)for each car.From a scatter plot made with the data,a linear model seemed appropriate.The following output was obtained from SPSS: Which of the following descriptions of the value of the slope is the correct description?

Deborah's Dairy Market sells both cottage cheese and ice cream.The sales manager recently noticed that in months when the company soldmore cottage cheese,it seemed to sell more ice cream as well,on average.One of the store's aides was assigned to put this theory to the test.The aide's analysis of sales data for the past 12 months (in millions of pounds for both the cottage cheese and the ice cream)gave the following SPSS output. Suppose the aide wishes to test the hypotheses H₀: ₁ = 0 versus H_a: ₁> 0.What is the value of the P-value for this test?

The moisture in a wet mix of cement was considered to have an effect on the denseness of the finished product.The moisture of the mix was controlled at various levels,and the denseness of the finished product was measured.The data were entered into SPSS,and the following output was generated. The standard error for the slope is reported to be 0.90.Which of the following interpretations of this standard error is correct?

Deborah's Dairy Market sells both cottage cheese and ice cream.The sales manager recently noticed that in months when the company soldmore cottage cheese,it seemed to sell more ice cream as well,on average.One of the store's aides was assigned to put this theory to the test.The aide's analysis of sales data for the past 12 months (in millions of pounds for both the cottage cheese and the ice cream)gave the following SPSS output. What is the equation of the least-squares regression line?

The statistical model for simple linear regression is written as ,where represents the mean of a Normally distributed response variable and x represents the explanatory variable.The parameters and are estimated,giving the linear regression model defined by ,with standard deviation  = 5. What is the range of values for 68% of the observed responses when x = 20 using the 68-95-99.7 rule?

There is an old saying in golf: "You drive for show and you putt for dough." The point is that good putting is more important than long driving for shooting low scores and hence winning money.To see if this is the case,data on the top 69 money winners on the PGA tour in 1993 are examined.The average number of putts per hole for each player is used to predict the total winnings (in thousands of dollars)using the simple linear regression model (1993 winnings)_i = ₀ + ₁(average number of putts per hole)_i + _i, Where the deviations _i are assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. Suppose the researchers conducting this study wish to estimate the 1993 winnings when the average number of putts per hole is 1.75.The following results were obtained from statistical software. If the researchers wish to estimate the winnings for a particular tour pro whose average number of putts per hole is 1.75,what would be a 95% prediction interval for the winnings?

A random sample of 79 companies from the Forbes 500 list (which actually consists of nearly 800 companies)was selected,and the relationship between sales (in hundreds of thousands of dollars)and profits (in hundreds of thousands of dollars)was investigated by regression.The following results were obtained from statistical software. What is an approximate 90% confidence interval for the slope ₁?

A recent study was done to assess factors that put Hispanic populations more at risk for obesity and related chronic diseases,such as diabetes and heart disease,than non-Hispanic populations.Data were collected on several factors,such as the crude morality rate of Hispanics,obesity prevalence,percent of adults diagnosed with diabetes,and median income at the state level.Pearson's Correlations were used to examine the strength of the relationship between obesity and the other variables,as a way of observing which characteristics were associated with high prevalence of obesity.In addition,a simple linear regression was used to model the relationship between diabetes and obesity.The results from SPSS are shown below. The largest diabetes rate is 14%.What is the predicted obesity rate?

The following scatter plot and SPSS output represent data collected on 89 middle-aged people.The relationship between body weight and percent body fat is to be studied. What is the value of the correlation between body fat and body weight?

There is an old saying in golf: "You drive for show and you putt for dough." The point is that good putting is more important than long driving for shooting low scores and hence winning money.To see if this is the case,data on the top 69 money winners on the PGA tour in 1993 are examined.The average number of putts per hole for each player is used to predict the total winnings (in thousands of dollars)using the simple linear regression model (1993 winnings)_i = ₀ + ₁(average number of putts per hole)_i + _i, Where the deviations _i are assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. The following (partial)ANOVA table was obtained from statistical software. What is the value of the F statistic for testing the hypotheses H₀: ₁ = 0 versus H_a: ₁  0?