2. Find the coefficient of correlation between price and sales from the foll data and interpret its valuc through probable error: Price : 103 85 92 90 84 88 90 93 98 95 Sales (units) : 800 500 610 700 630 670 800 750 700 680
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- An economist want to determine the relation between one’s FICO score, x, and the interest rate of a 36-month auto loan, y. The given data represent the interest rate (in percent) a bank would offer on a 36-month auto load for various FICO scores. Credit Score;x Interest Rate (percent);y 545 18.982 595 17.967 640 12.218 675 8.612 705 6.68 750 5.15 Find the least-squares regression line treating the FICO score as the explanatory variable and the interest rate as the response variable. Predict the interest rate a person would pay if their FICO score were the median score of 723.An economist want to determine the relation between one's FICO score, x, and the interest rate of a 36-month auto loan, y. The given data represent the interest rate (in percent) a bank would offer on a 36-month auto load for various FICO scores. Credit Interest Rate Score;x (percent);y 545 18.982 595 17.967 12.218 8.612 705 6.68 750 5.15 1. Find the least-squares regression line treating the FICO score as the explanatory variable and the interest rate as the response variable. 2. Predict the interest rate a person would pay if their FICO score were the median score of 723. 640 675An insurance company determines that a linear relationship exists between the cost of fire damage in major residential fıres and the distance from the house to the nearest fire station. A sample of 15 recent fires in a large suburb of a major city was selected. For each fire, the following variables were recorded: x= the distance between the fire and the nearest fire station (in miles) y= cost of damage (in dollars) The distances between the fire and the nearest fire station ranged between 0.7 miles and 6.1 miles. The correlation between cost and distance is 0.961. Test if the correlation is significant at a=.10. O No, the correlation is not significant because 0.961 does not exceed the critical value. O Yes, the correlation is significant because 0.961 exceeds the critical value. No, the correlation is not significant because 0.961 exceeds the critical value. O Yes, the correlation is significant because 0.961 does not exceed the critical value. O No, the correlation is not…
- A farmer in Indiana wants to examine the relation between the number of very hot days (days when the high temperature exceeds 95° F) and the corn production of his farm (in bushels of corn per acre). He looks at the data for 10 summers. Let x¡ = the number of hot days during the ith summer. %3D = the corn production (in bushels per acre) during the ih summer. Let yi The data are in the table below:. 4 6. 7 8. 9. 10 i 2 14 10 7. 8. 1 12 Xi Yi 95 80 83 87 88 85 99 102 79 95 a) Make a scatterplot of the data. b) Examine your scatterplot and, without performing any calculations, EXPLAIN whether you expect the correlation coefficient to be closer to -1, 0, or 1 and WHY. c) Find the sample mean and standard deviation for each variable. %3D %3D S. %3D y d) Place an asterisk on your scatterplot at the point (x,ỹ).A real estate agency collects the data in the following table concerning y = sales price of a house (in thousands of dollars) x1 = home size (in hundreds of square feet) x2 = rating (an overall "niceness rating" for the house expressed on a scale from 1 [worst] to 10 [best], and provided by the real estate agency) Sales Price, y (x $1000) 180 98.1 173.1 136.5 141 165.9 193.5 127.8 163.5 172.5 Home Size, x₁ (x 100 ft²) Modell: y Bo + B₁x₁ + B₂X₂ +€ Model2: y Bo + B₁x₁ + B₂x₂ + B3x² + € = 23 11 20 17 15 21 24 13 19 25 Rating, X₂ Make a comparison between models: (f) Based on their Råbj (g) Based on their C.I and P.I. 86966 ∞ WONt 2 9 3 8 4 7 The agency wishes to develop a regression model that can be used to predict the sales prices of future houses it will list. 2 Use software of your choice to fit the 2 following models. Then answer the same questions (a-e) for both models. (a) Discuss why scatter plot of y vs x₁ and x₂ indicate that this model might be reasonable. (b) Interpret the…The amount of time adults spend watching television is closely monitored by firms because this helps to determine advertising pricing for commercials. Complete parts (a) through (d). (a) Do you think the variable "weekly time spent watching television" would be normally distributed? If not, what shape would you expect the variable to have? A. The variable "weekly time spent watching television" is likely skewed left, not normally distributed. B. The variable "weekly time spent watching television" is likely normally distributed. C. The variable "weekly time spent watching television" is likely uniform, not normally distributed. D. The variable "weekly time spent watching television" is likely symmetric, but not normally distributed. E. The variable "weekly time spent watching television" is likely skewed right, not normally distributed.
- The scatter plot shows the sizes and annual rents of some office spaces in the downtown area of a city. Rent (dollars) 140,000 105,000 70,000 35,000 SIZE AND ANNUAL RENT OF OFFICE SPACE ¡. 1: 0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 Office Space (square feet) What would the line of best fit reveal about these data? There is a strong positive relationship between the cost of rent and the size of the office space. There is a strong negative relationship between the cost of rent and the size of the office space. O There is a weak negative relationship between the cost of rent and the size of the office space. O There is a weak positive relationship between the cost of rent and the size of the office space.The amount of time adults spend watching television is closely monitored by firms because this helps to determine advertising pricing for commercials. Complete parts (a) through (d). (a) Do you think the variable "weekly time spent watching television" would be normally distributed? If not, what shape would you expect the variable to have? A. The variable "weekly time spent watching television" is likely normally distributed. B. The variable "weekly time spent watching television" is likely skewed right, not normally distributed. C. The variable "weekly time spent watching television" is likely symmetric, but not normally distributed. D. The variable "weekly time spent watching television" is likely skewed left, not normally distributed. E. The variable "weekly time spent watching television" is likely uniform, not normally distributed. (b) According to a certain survey, adults spend 2.35 hours per day watching television on a weekday. Assume that the standard deviation for "time spent…The scatter plot shows the relationship between the number of minutes studying for a test (x) and the number of mistakes made (y). The graph shows the scatterplot of the data and a fitted line. 17 16 15 14 13 12 10 용 5- 4- 3- 10 20 30 40 50 60 70 80 90 100 110 120 Select True or False for each statement based on the scatter plot. True/False There is a positive association between the amount of time studying for a test and the number of mistakes made. True False Students who studied for a longer period of time tended to make less mistakes. True False There is a linear association between time True False studying and number of mistakes.
- Find the trend line equation and obtain the trend values for the following data using the method of least square. Also forecast the earning for 2000. Year : 1991 | 1992 | 1993 | 1994 1995 | 1996 | 1997 | 1998 69 Earning (in '000 Rs.) : 38 40 65 72 60 87 95A scatter plot would be useful for: Showing the relationship between the sales of blank CDs and blank DVDs Showing the trend of sales, over time, of five different brands of blank DVDs Showing the relative number of sales of four different brands of blank DVDs Showing the top selling brands of blank DVDsBelow is a table showing the relationship between age and bone density of a typical healthy adult male. Age (years) 25 35 45 55 65 75 85 Bone density (mg/cm²) 1165 1135 1085 1060 1015 975 910 Using your line of best fit find the equation for this line. Describe the correlation between the two variables and what conclusions can you make from this set of data? Using graph plotted extrapolate to find the bone density of a 90 years old typical adult.