In a study of the relationship between real aggregate consumption and pricesin a specific country based on a time series of 104 observations, the followingOLS regression function was obtained (standard errors in parentheses),C; = 13.74 + 0.24P,(0.35)R = 0.12,SER= 2.85,(1)(0.05)where C, is logarithm of consumption and P, is logarithm of price.(a) Is the coefficient on P statistically significant?(b) Compute the p-value for the test of significance of the coefficient on P.(c) Comment on the sign of the coefficient on P.

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Answered: In a study of the relationship between…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 1TI: Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use...

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What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
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?
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age in years (X1) and their gender (X2) (0 if male and 1 if female). The yearly income of a 24-year-old female individual is
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.
Consider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary=11,149.90+2524.17(Education)+1104.17(Experience) Suppose an employee with 12 years of education has been with the company for 11 years (note that education years are the number of years after 8th grade). According to this model, what is his estimated annual salary?
Suppose you obtain the following regression model, E[y]=91+79*x1 +20*x1*x2. What is the impact of a 39 unit change of x1 on the expected value of y when x2 is at its mean of 40?
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 7
Fit a linear-regression model relating annual inci- dence of diabetes to time period. (For this purpose, score the time period as 1 if 1970−1974, 2 if 1975−1979, . . . , 5 if 1990−1994.)
The following table is adapted from a paramecium culture experiment conducted by Gause in 1934. The data show the paramecium population N as a function of time t in days. Use regression to find a logistic model for this population using a graphing calculator. Round the r value to three decimal places and the other parameters to two decimal places. t N 2 24 3 35 5 95 6 193 8 350 9 428 10 520 11 580 a) N = 83.54 / 1+680.87e^-0.558t b) N = 681.87 / 1+83.54e^-0.558t c) N = 680.87 / 1+83.54e^-0.558t d) N = 83.54 / 1+0.558e^-0.558t
Consider the following regression analysis between sales (Y in $1,000) and social media advertising (X in dollars).Ŷ = 55,000 + 7XThe regression equation implies that an ________. Multiple Choice increase of $7 in advertising is associated with an increase of $7,000 in sales increase of $1 in advertising is associated with an increase of $7 in sales increase of $1 in advertising is associated with an increase of $62,000 in sales increase of $1 in advertising is associated with an increase of $7,000 in sales
Consider the following hypothetical regression, with FAIL? as a dummy variable for if a business failed in its first year (1=failed, 0=didn’t fail); LOAN is how much money, in thousands of dollars, the business got as a loan when it started; GIG? is a dummy variable for if there was a gig economy job available, such as driving for Lyft (1=available, 0=not available), and COMP is the number of existing competitors the business faced when it started. All variables are statistically significant. FAIL? = 0.63 – 0.01*LOAN – 0.08*GIG? + 0.05*COMP Answer the following: Determine the predicted value of FAIL? if the business had a $30,000 loan, there was no gig economy, and four competitors. In everyday language, what does the estimated value found in A mean? If a business gets an additional six thousand dollars in loans, how would FAIL? change? Give the “punchline” interpretation of the COMP variable: “For every additional competitor…”
Consider the following regression equation representing the linear relationship between the Canada Child Benefit provided for a married couple with 3 children under the age of 6, based on their annual family net income: ŷ =121.09−0.57246xR2=0.894 where y = annual Canada Child Benefit paid (in $100s) x = net annual family income (in $1000s) Source: Canada Revenue Agency a. As the net annual family income increases, does the Canada Child Benefit paid increase or decrease? Based on this, is the correlation between the two variables positive or negative?The Canada Child Benefit paid .The correlation between the two variables is .b. Calculate the correlation coefficient and determine if the relationship between the two variables is strong, moderate or weak.r= , the relationship is . Round to 3 decimal places c. Interpret the value of the slope as it relates to this relationship. For every $1 increase in annual family net income, there is a $0.57246 decrease in…

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