Find a formula for a power function that models the following data. (Round the regression parameters to two decimal places.) f(x) = f = 0.4 x x2.26 f = 0.31 x x2.4 f = 0.3 x x2.35 f = 0.33 x x2-.32 O f = 0.39 xx2.28 х 2 4 4.6 0.3 1.8 8.1 12.3
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- 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?The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
- Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. Using the 68-95-99.7 rule, between what two values would approximately 95% of the observed responses, y, fall when x = 7?A surgery intern has conducted a study of the sleeping habits of her colleagues and has developed a following regression equation: y-hat = 6 + 0.1X, where X is the number of hours working on one shift, and Y is the number of hours sleeping at night after that shift. Yvette worked 10 hours and slept 8 hours. What is Yvette’s residual? 0.1 1 6 7The birth lengths in cm (x) and birth weights in kg (y) of a sample of 50 newborn female babies are compared, yielding a correlation coefficient of r=0.578 and a linear regression equation of ŷ =−8.89+0.243x The babies all had lengths between 46.5 and 53.0 cm, and weights between 2.50 and 4.05 kg. Based on this, predict the birth weight of a newborn female baby with a birth length of 48.5 cm.
- An investigation into the relationship between an adolescent mother's age x in years and the birth weight y of her baby in grams yielded the regression equation y= - 1163.45 + 245.15x as well as r = .88369, r2= .78091, SSE = 337212.45, and s= 205.30844 1) What is the predicted birth weight for a baby brn to a 17 year old woman? 2) What is the propotion of the variability in the weights of babies born to adolescent mothers that is accounted for by the mother's age? 3) For every additional year in the mother's age that mean birth weight of the baby? (a) increases by about 245g (b) decreases by about 245g (c) increases by about 1163g (d) increases by about 1163g (e) changes by an amount that cannot be determined from the information given.The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is _____.The quadratic regression equation shown below is for a sample of n=22. Determine the critical value(s).
- 1) Find the regression equation and r value Drop Height, y (m) Square of Mean Fall time, t^2 (s^2) 0.100 0.0188 0.300 0.0576 0.500 0.0980 1.000 0.198 1.500 0.305 2.500 0.508The table below shows the results of an experiment involving the growth of bacteria. Write a power regression equation for this set of data, rounding all values to three decimal places. Using this equation, predict the following… The bacteria’s growth, to the nearest integer, after 15 minutes. The amount of time, to the nearest minute, for there to be 4,000 bacteria present.Use the following linear regression equation to answer the questions. (d) x1 = 1.0 + 3.9x2 – 8.4x3 + 2.4x4 Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?Suppose x2 increased by 2 units. What would be the expected change in x1?Suppose x2 decreased by 4 units. What would be the expected change in x1?(e) Suppose that n = 8 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.468. Construct a 90% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 5%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t t critical ±