An article in the journal of Monetary Economics assesses the relationship between percentage growth in wealth over a decade and a half of saving for baby boomers of age 40 to 55 with these people's income quartiles. The article present table showing five income quartiles and for each quartile there is s reported percentage growth in wealth. The data are as follows.
Income quartile: 1 2 3 4 5
Wealth Growth(%): 17.3 23.6 40.2 45.8 56.8
Run a simple linear regression of these five pairs of numbers and estimate a linear relationship between income and percentage growth in wealth.
The following are data in annual inflation and stock returns. Run a regression analysis of the data and determine whether there is a linear relationship between inflation and total return on stocks for the periods under study.
Inflation Total return on stocks (%)
An article in Worth discusses the immense success of one of the world's most prestigious cars, the Aston Martin Vanquish. This car is expected to keep its value as it age. Although this model is new, the article reports resale values of earlier Aston Martin models over various decades.
Decade : 1960s 1970s 1980s 1990s 2000s
(Average): $180,000 $40,000 $60,000 160,000 $200,000
Based on these limited data, is there a relationship between age and average price of an Aston Martin? What are the limitations of this analysis? Can you think of some hidden variables that could affect what you are seeing in the data?
Give 95% confidence intervals for the regression slope and the regression intercept parameters for the situation of problem 10-11
Compute the sample correlation coefficient for the data of problem 10-11
A study was conducted to determine whether a correlation exist between consumers' perceptions of a television commercial (measured on a special scale) and their interest in purchasing the product (measured on a scale). The results are n=65 and r=0.37. Is there statistical evidence of a linear correlation between the two variables?
A regression analysis was carried out on returns on stocks (Y) versus the ratio of book to market value (X). The resulting prediction equation is
Y=1.21 + 3.1X(2.89)
Where the number parentheses is the standard error of the slope estimate. The sample size used is n=18. Is there evidence of a linear relationship between returns and book to market value?
In the situation of problem 10-1, test for the existence of a linear relationship between the two variables.
What percentage of the variation in percent growth in wealth is explained by the regression in problem 10-11?
Conduct the F test for the existence of a linear relationship between the two variables in problem 10-11.
Conduct an F test for the existence of e linear relationship in the case of problem 10-15.
For problem 10-11, give a point prediction and a 99% prediction interval for wealth growth when the income quartile is 5.
Complete, Neat and Step-by-step Solutions are provided in the attached Excel file.