1. The scatterplot shows the relationship between latitude and mean July temperature (in degrees Fahrenheit) for 12 cities in the United States. The equation of the regression line relating these variables is y 106.5-0.782x %3D 95 90 85: 80 75- 70 30 32 34 36 38 40 42 Latitude (degrees) a) Predict the mean July temperature in Fairbanks, Alaska, at latitude 65°. How confident are you in this prediction? Explain. b) Los Angeles, California, is at latitude 34° and has a mean July temperature of 74°. Calculate its residual. c) Interpret the slope of the regression line. d) Does the value of the y intercept have meaning in this context? If so, interpret the y intercept. If not, explain why. Mean July temperature ("F)

1. The scatterplot shows the relationship between latitude and mean July temperature (in degrees Fahrenheit) for 12 cities in the United States. The equation of the regression line relating these variables is y 106.5-0.782x %3D 95 90 85: 80 75- 70 30 32 34 36 38 40 42 Latitude (degrees) a) Predict the mean July temperature in Fairbanks, Alaska, at latitude 65°. How confident are you in this prediction? Explain. b) Los Angeles, California, is at latitude 34° and has a mean July temperature of 74°. Calculate its residual. c) Interpret the slope of the regression line. d) Does the value of the y intercept have meaning in this context? If so, interpret the y intercept. If not, explain why. Mean July temperature ("F)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value? Chirps in 1 min 784 838 822 949 1188 813 Temperature (°F) 65.7 67.8 66.2 79.9 92.3 73.5 What is the regression equation? What is the best-predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute? The best predicted temperature when a bug is chirping at 3000chirps per minute are? What is wrong with this predicted value? Choose the correct answer below. A. It is unrealistically high. The value 3000 is far outside of the range of observed values. B. The first variable should have been the dependent variable. C. It is only an…
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. x 11.8 8.2 6.9 3.9 2.3 2.4 2.6 0.6 y 14.2 11.2 10.2 7.5 5.9 6.4 6 4.3 x = thousands of automatic weaponsy = murders per 100,000 residents This data can be modeled by the equation y=0.88x+3.95. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator. A) How many murders per 100,000 residents can be expected in a state with 7.2 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 1.6 thousand automatic weapons? Answer = Round to 3 decimal places.
Researchers are interested in predicting the height of a child based on the heights of their mother and father. Data were collected, which included height of the child (height ), height of the mother ( mothersheight), and height of the father (fathersheight ). The initial analysis used the heights of the parents to predict the height of the child (all units are inches). The results of the analysis, a multiple regression, are presented below. . regress height mothersheight fathersheight Source Model Residual Total height mothersheight fathersheight _cons SS df 208.008457 314.295372 37 2 104.004228 8.49446952 MS 522.303829 39 13.3924059 Coef. Std. Err. .6579529 .1474763 .2003584 .1382237 9.804327 12.39987 t P>|t| 4.46 0.000 C 0.156 0.79 0.434 Number of obs = F( 2, 37) = Prob > F R-squared Adj R-squared Root MSE = .3591375 -.0797093 -15.32021 = 40 12.24 0.0001 0.3983 0.3657 2.9145 [95% Conf. Interval] .9567683 .4804261 34.92886 What is the predicted height for a child born to a mother…
The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value? Chirps in 1 min 760 1119 1125 850 965 785 D Temperature (°F) 70.5 90.8 90.8 74.7 77.1 69.9 What is the regression equation? (Round the x-coefficient to four decimal places as needed. Round the constant to two decimal places as needed.)
The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best-predicted temperature for a time when a bug is chirping at the rate of 3000chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value? Chirps in 1 min 1004 952 1237 1116 1177 1249 Temperature (°F) 83.1 76 95.1 87.5 92.1 88.4 What is the regression equation? (^ over y)=_____+_____x (Round the x-coefficient to four decimal places as needed. Round the constant to two decimal places as needed.) What is the best-predicted temperature for a time when a bug is chirping at the rate of 3000chirps per minute? The best-predicted temperature when a bug is chirping at 3000 chirps per minute is ____°F. (Round to one decimal place as needed.) What is wrong with this predicted value? Choose the correct answer below. A. It is…
A marketing consultant created a linear regression model to predict the number of units sold by a client based on the amount of money spent on marketing by the client. Which of the following is the best graphic to use to evaluate the appropriateness of the model?
Develop a scatterplot and explore the correlation between customer age and net sales by each type of customer (regular/promotion). Use the horizontal axis for the customer age to graph. Find the linear regression line that models the data by each type of customer. Round the rate of changes (slopes) to two decimal places and interpret them in terms of the relation between the change in age and the change in net sales. What can you conclude? Hint: Rate of Change = Vertical Change / Horizontal Change = Change in y / Change in x
The table shows the lengths and weights of seven muskies captured by the Department of Natural Resources in Catfish Lake in Eagle River, Wisconsin. Use the linear regression feature on a graphing calculator to determine an equation of the line that best fits the data. Round to the hundredths. Musky 1 2 3 4 5 6 7 Length (in.) 26 27 29 33 35 36 38 Weight (lb) 5 8 9 12 14 14 19
Below is the actual data on the speed a person walks or runs in miles/hour and the calories the person burns per lap. Find the linear equation of best fit for this data. Compare the model to the data. Does the model seem to fit the data? Explain. What is the significance of the y-intercept? What is the slope and what does it mean? What is the x-intercept and what does it mean? What is the correlation coefficient and what does it mean? Speed (mph) Calories/lap 1 42 2 31 3 27 4 41 5 40 6 40 7 39 8 38 r answers to the nearest hundredth. The y-intercept means that if a person runs at ----------mph they will burn__________ per lap. The slope means that for each mph you increase your speed, you will burn an additional------------calories pay lap
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Range of ankle motion is a contributing factor to falls among the elderly. Suppose a team of researchers is studying how compression hosiery, typical shoes, and medical shoes affect range of ankle motion. In particular, note the variables Barefoot and Footwear2. Barefoot represents a subject's range of ankle motion (in degrees) while barefoot, and Footwear2 represents their range of ankle motion (in degrees) while wearing medical shoes. Use this data and your preferred software to calculate the equation of the least-squares linear regression line to predict a subject's range of ankle motion while wearing medical shoes, ?̂ , based on their range of ankle motion while barefoot, ? . Round your coefficients to two decimal places of precision. ?̂ = A physical therapist determines that her patient Jan has a range of ankle motion of 7.26°7.26° while barefoot. Predict Jan's range of ankle motion while wearing medical shoes, ?̂ . Round your answer to two decimal places. ?̂ = Suppose Jan's…
A financial website reported the beta value for a certain company was 0.86. Betas for individual stocks are determined by simple linear regression. The dependent variable is the total return for the stock, and the independent variable is the total return for the stock market, such as the return of a market index. The slope of this regression equation is referred to as the stock's beta. Many financial analysts prefer to measure the risk of a stock by computing the stock's beta value. Suppose the following data show the monthly percentage returns for the market index and the company for a recent year. Month Market Index% Return Company% Return August -3 4 September 8 7 October 0 1 November -2 1 December -5 0 January 0 0 February 7 7 March 0 -2 April 2 0 May -5 -1 a. Develop the least squares estimated regression equation. (Let x = Market Index % Return (as a %), and let y = Company % Return (as a %). Round your numerical values to four decimal places.)