Interpreting technology: The following display from the TI-84 Plus calculator presents the least-squares regression line for predicting the price of a certain stock (y) from the prime interest rate in percent (x). LinReg y=a+bx a=2.38968653 b=0.3961407 2 ,² = 0.4053168942 r r 0.63664503
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1. Find regression line equation
2. What is the
3. Predict the price when the prime interest rate is 7%. Round the answer to at least four decimal places.
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- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
- Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. In each case, there is sujficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. Altitude and Temperature Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded by the author during Delta Flight 1053 from New Orleans to Atlanta. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet).
- The data shown below are the initial weights and gains in weight (in grams) of female rats on a high protein diet from 24 to 84 days of age. The point of interest in these data is whether the gain in weight is related to (dependent on) the initial weight. If so, then feeding experiments on female rats can be made more precise by adjusting for differences in initial weights of the rats. Statistically test this with a regression analysis. Rat Number Initial Weight (gms) Weight Gain (gms) 1 50 128 2 64 159 3 76 158 4 64 119 5 74 133 6 60 112 7 69 96 8 68 126 9 56 132 10 48 118 11 57 107 12 59 106 13 46 82 14 45 103 15 65 104 I used excel's regression took pak and got the following: SUMMARY OUTPUT Regression Statistics Multiple R 0.489416452 R Square 0.239528464 Adjusted R Square 0.181030653 Standard Error 8.869929833 Observations 15…The following data give the yearly inflation rate and money supply growthrate (both measured in percentage) for 51 countries. A simple regression of Infla-tion on Growth yields the following information from RegressIt output: (a) What is the linear relationship implied by these data? (b) For a country with an 6% money supply growth, what would be theexpected inflation? (This means Growth= 6 as it is measured in percentage.) (c) A simplistic monetarist claims that a 1% increase in the money supplygrowth rate would result in a corresponding 1% increase in inflation. In otherwords, for the relationship of Inflation = β0 + β1Growth, the null hypothesis isβ1 = 1. Do the regression results support this null hypothesis?The following regression equation gives the relationship between the number of Fake Christmas trees sold each year in a certain state and the number of Real Christmas trees sold that same year in that state: Fake = 8162 - 0.11(Real)(a) How many fake Christmas trees would you predict for a year in which 9211 real Christmas trees sold? (2 decimal places) (b) This model has an R-squared value of 0.1. What is the correlation between the number of real and fake trees sold? (3 decimal places) (c) A competing model predicting the number of fake trees sold using the number families with children under age 8 has an R-squared value of 0.21. Which model should we prefer? We should prefer the model using the number of real trees sold.We should prefer the model using the number of children under age 8. We should not have a preference between the two models.
- You have been assigned the task of comparing the investment performance of five different pension fund managers. After gathering 60 months of excess returns (returns in excess of the monthly risk-free rate) on each fund as well as the monthly excess returns on the entire stock market, you perform the regressions of the form: (Rfund - RFR)t = a + B(Rmkt - RFR)t + et You have prepared the following summary of the data, with the standard errors for each of the coefficients listed in parentheses. Regression Data (Rfund - RFR) Portfolio a B R^2 Mean o ABC 0.192 1.048 94.1% 1.022% 1.193% (0.11) (0.10) DEF -0.053 0.662 91.6% 0.473% 0.764% (0.19) (0.09) GHI 0.463 0.594 68.6% 0.935% 0.793% (0.19) (0.07) JKL 0.355 0.757 64.1% 0.955% 1.044% (0.22) (0.08) (MNO) 0.296 0.785 94.8% 0.890% 0.890% (0.14) (0.12) a. Which fund had the highest degree of diversification over the sample period? How is…2) The following results are an autoregression for US Exports to Mexico where the dependent variable is the lagged value of US Exports. Based on these regression results, what is your forecast of US Exports to Mexico for March 2005?The least-squares regression equation is y = 689.9x + 14,803 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7256. Complete parts (a) through (d). (a) Predict the median income of a region in which 20% of adults 25 years and older have at least a bachelor's degree. (Round to the nearest dollar as needed.) . TOLED dian Income Media 55000- 20000- 15 20 25 30 35 40 45 50 55 60 Bachelor's 96 Q