An engineer wants to determine how the weight of a car, x, affects gas mileage, y. The following data represent the weights of various cars and their miles per gallon. Car B 2625 2935 3260 3860 4130 27.6 26.6 21 D Weight (pounds), X Miles per Gallon, y 20.2 18.8 (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. Write the equation for the least-squares regression line. (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.) (b) Interpret the slope and intercept, if appropriate. Choose the best interpretation for the slope. O A. The slope indicates the mean miles per gallon. O B. The slope indicates the mean weight O C. The slope indicates the mean change in miles per gallon for an increase of 1 pound in weight. O D. The slope indicates the ratio between the mean weight and the mean miles per gallon O E. It is not appropriate to interpret the slope because it is not equal to zero. Click to select your answer(s)

The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r= - 0.977. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is -0.0061x +41.3297. Complete parts (a) and (b) below. V = Click the icon to view the data table. (a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is %. (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. % of the variance in is by the linear model. (Round to one decimal place as needed.) Data Table Full data set Miles per Miles per Weight (pounds), x Weight (pounds), x Car Car Gallon, y Gallon, y 1…

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The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 6 varieties of granola bars.Sugar (grams) 4 12 8 7 14 6 Calories 120 140 120 180 190 80 a. Decide which variable should be the independent variable and which should be thedependent variable. Justify your decision. (2 marks) e. Write down the regression equation. (1 mark)f. Find and interpret the coefficient of determination. (3 marks)g. Use the 10% level of significance to examine whether the independent variable is a goodpredictor for the dependent variable. In responding, state the null hypothesis(es), thedecision rule and make the decision for each hypothesis. (5 marks)h. Would the simple regression be useful in predicting calories given the amount of sugar of 5 grams? In responding, state the null hypothesis(es), the decision rule for α = 0.05 and make the decision for each hypothesis. (5 marks)

A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below: City Price ($) Sales River Falls 1.30 100 Hudson 1.60 90 Ellsworth 1.80 90 Prescott 2.00 40 Rock Elm 2.40 38 Stillwater 2.90 32 What is the test statistics for testing the significance of correlation coefficient? a e W ch

Read the following description of a data set. The owner of a bicycle store wonders if the employees who take the longest lunch breaks also make the fewest bicycle sales. One day, she notes the length of each salesperson's lunch break (in minutes), x, as well as the number of bicycles he or she sold that day, y. The least squares regression line of this data set is: ŷ = -0.297x + 10.889 Complete the following sentence: If a salesperson spends one additional minute at lunch, the least squares regression line predicts he or she will sell | fewer bicycles that day. Submit е

The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) through (c) below. Click the icon to view the data table. ..... (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. y =x+O %D/ (Round the x coefficient to three decimal places as needed. Round the constant to the nearest integer as needed.) Find the least-squares regression line for females. y = ý =x+O %3D (Round the x coefficient to three decimal places as needed. Round the constant to the nearest integer as needed.) (b) Interpret the slope of the least-squares regression line for each gender, if appropriate. How might an insurance company use this information? What is the correct interpretation of the…

A study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected. Number ofFacilities AverageDistance(miles) 9 1.65 11 1.11 16 0.83 21 0.62 27 0.51 30 0.48 (a) Develop a scatter diagram for these data, treating average distance traveled as the dependent variable. A scatter diagram has 6 points. The horizontal axis ranges from 0 to 1.8 and is labeled: Distance. The vertical axis ranges from 5 to 35 and is labeled: Number. Moving from left to right, the leftmost point is at approximately (0.48, 30), with the next five points extending downward. The points decrease steeply at first and then level off.   A scatter diagram has 6 points. The horizontal axis ranges from 5 to 35 and is labeled: Number. The vertical axis ranges from 0 to 1.8 and is labeled: Distance. Moving from left to right, the leftmost point is at…

Corvette, Ferrari, and Jaguar produced a variety of classic cars that continue to increase in value. The data showing the rarity rating (1–20) and the high price ($1000s) for 15 classic cars is contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.     Open spreadsheet   Develop a scatter diagram of the data using the rarity rating as the independent variable and price as the dependent variable. Does a simple linear regression model appear to be appropriate?   A simple linear regression model _________appearsdoes not appear to be appropriate. Develop an estimated multiple regression equation with  rarity rating and  as the two independent variables.        (to whole numbers) What is the value of the coefficient of determination? Note: report  between 0 and 1.  (to 3 decimals) What is the value of the  test statistic?  (to 2 decimals) What is the -value?  (to 4 decimals) Consider the nonlinear relationship shown by equation .…

An engineer wants to determine how the weight of a​ car, x, affects gas​ mileage, y. The following data represent the weights of various cars and their miles per gallon. Car A B C D E   Weight​ (pounds), x 2725 2875 3270 3715 4135 Miles per​ Gallon, y 27.4 23.3 22.9 20.5 18.7 ​(a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. Write the equation for the​ least-squares regression line.   y=__ x+__   ​(Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as​ needed.)