4.7 Consider the simple linear regression model fit to the weight and blood pressure data in. Symbolic BP Subject Weight Subject Weight Systolic BP 1 165 130 14 172 153 2 167 133 15 159 128 3 180 150 16 168 132 4 155 128 17 174 149 5 212 151 18 183 158 6 175 146 19 215 150 7 190 150 20 195 163 8 210 140 21 180 156 9 200 148 143 124 10 149 125 240 170 11 158 133 235 165 12 169 135 25 192 160 13 170 150 26 187 159 a. Construct a normal probability plot of the residuals. Does there seem to be any problem with the normality assumption? เสีสสสสส 22 23 24
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- The following is part of the computer output from a regression of monthly returns on Waterworks stock against the S&P 500 Index. A hedge fund manager believes that Waterworks is underpriced, with an alpha of 2% over the coming month. Beta R-square Standard Deviationof Residuals 0.75 0.65 0.06 (i.e., 6% monthly) Now suppose that the manager misestimates the beta of Waterworks stock, believing it to be 0.50 instead of 0.75. The standard deviation of the monthly market rate of return is 5%. Required: a. If he holds a $6 million portfolio of Waterworks stock and wishes to hedge market exposure for the next month using one-month maturity S&P 500 futures contracts, what is the standard deviation of the (now improperly) hedged portfolio? The S&P 500 currently is at 3,000 and the contract multiplier is $50. (Do not round intermediate calculations. Round your percentage answer to 2 decimal places.) b. What is the probability of incurring a loss over the next month…A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.34. A dietician is asked to test this claim and finds that a random sample of 16 servings has a variance of 1.22. At α=0.05, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below.A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.33. A dietician is asked to test this claim and finds that a random sample of 24 servings has a variance of 1.37. At α=0.01, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below. (a) Write the claim mathematically and identify H0 and Ha. A. H0: σ2≤1.33 (Claim) Ha: σ2>1.33 B. H0: σ2≠1.33 Ha: σ2=1.33 (Claim) C. H0: σ2≥1.33 Ha: σ2<1.33 (Claim) D. H0: σ2=1.33 (Claim) Ha: σ2≠1.33 (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is(are) enter your response here. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Choose the correct statement below and fill in the corresponding answer boxes. A. The…
- Suppose that a sample of n = 12 pairs of X and Y scores has SSY = 90 and a Pearson correlation of r = +0.40. Does the regression equation predict a significant portion of the variance? Test with α = .05.(hint: SStotal = SSY; r2 = SSregression/SSTotal)A researcher conducts an independent- measures research study and obtains t = 2.070 with df = 28. How many individuals participated in the entire research study? Using a two- tailed test with α = .05, is there a significant difference between the two treatment conditions? Compute r2 to measure the percentage of variance accounted for by the treatment effect.In a sample of 12 randomly selected high school seniors, the mean score on a standardized test was 1200 and the standard deviation was 160.5. Further research suggests that the population mean score on this test for high school seniors is 1016. Does the t-value for the original sample fall between −t0.90 and t0.90? Assume that the population of test scores for high school seniors is normally distributed.
- Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H0)?(i) Heteroskedasticity.(ii) A sample correlation coefficient of .95 between two independent variables that are in the model.(iii) Omitting an important explanatory variable.A sample of n = 120 scores were presented using the Tenacity (authority) scores to the following predictors: age gender, SES, tone of voice, and clothing. Using a two-tailed test at the 0.05 level of significance, a multiple regression analysis was computed: 1. tenacity and age (pvalue = 0.043); 2. tenacity and gender (pvalue = 0.102); 3. tenacity and SES (pvalue = 0.40); 4. tenacity and voice (pvalue = 0.001); 5. tenacity and clothing (value = 0.017); SOrs Using the pvalue, provide your DECISION, whether:Accept Ho or Reject Ho, Accept HaA snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.25. A dietician is asked to test this claim and finds that a random sample of 22 servings has a variance of 1.35. At ⍶ = 0.05 is there enough evidence to reject the manufacturer’s claim?
- The random sample of 7 pairs of observations from the normal population gives the following information:- x 8 1 3 6 12 7 10 y 13 30 23 35 24 18 15 [ r = -0.459 and take the significance level (alpha) = 0.02] The P - Value of the test statistic ( along with decision ) used for testing that the two variables are not linearly related ( H(null) : roll = 0) isA snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.141.14. A dietician is asked to test this claim and finds that a random sample of 2424 servings has a variance of 0.950.95. At alpha equals 0.10α=0.10, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed.Given are five observations for two variables, x and y. xi 2 7 15 18 20 yi 60 51 42 12 14 Use the estimated regression equation: y^=68.5866-2.6441 . a. Compute the mean square error using equation. (to 4 decimals) b. Compute the standard error of the estimate using equation. (to 4 decimals) c. Compute the estimated standard deviation of b1 using equation. (to 4 decimals) d. Use the t-test to test the following hypotheses (a=0.05): Compute the value of the t-test statistic (Enter negative values as negative numbers). (to 3 decimals) What is the p-value? Use Table 2 from Appendix B. p-value is What is your conclusion? We (do not reject, reject). e. Use the F-test to test the hypotheses in part (d) at a 0.05 level of significance. Complete the F table below using Excel. Calculate the Sum of Squares (to 1 decimal), the Mean Squares (to 1 decimal), and the F ratio (to 2 decimals) and the p-value (to 4 decimals). Sourceof Variation Degreesof Freedom Sum ofSquares MeanSquare F…