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question:Calculate the slope and y-intercept for a least-squares line. The following table shows the relationship between weight and calories burned per minute for five people. Weight (in pounds) Calories burned per minute 112 7.25 129 9.15 150 9.85 174 10.25 182 11.75 Mean 149.4 9.65 Standard Deviation 29.51 1.64 Weight is the explanatory variable and has a mean of 149.4 and a standard deviation of 29.51. Calories burned per minute is the response variable and has a mean of 9.65 and a standard deviation of 1.64. The correlation was found to be 0.944. Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place.

answer:The slope of the least-squares line can be calculated using the formula: slope = r * (SD of y / SD of x) where r is the correlation coefficient and SD is the standard deviation. So, slope = 0.944 * (1.64 / 29.51) = 0.053 To find the y-intercept, we can use the formula: y-intercept = mean of y - slope * mean of x y-intercept = 9.65 - 0.053 * 149.4 = 1.94 Therefore, the slope of the least-squares line is 0.05 and the y-intercept is 1.94 (rounded to the hundredths place).

question:Interpret the slope of a regression line. Blake enters data for weight (in hundreds of pounds) and miles per gallon of cars into a statistics software package and finds a regression equation of ŷ = 38.5 - 1.4x, where weight is the explanatory variable. Based on this information, select Blake's conclusion about weight and miles per gallon that is TRUE. a.) For each additional one pound of weight, miles per gallon stays relatively the same. b.) For each additional one hundred pounds of weight, miles per gallon decreases by 1.4 miles. c.) For each additional one hundred pounds of weight, miles per gallon increases by 1.4 miles. d.) For each additional one hundred pounds of weight, miles per gallon decreases by 38.5 miles.

answer:b.) For each additional one hundred pounds of weight, miles per gallon decreases by 1.4 miles. The slope of the regression line represents the change in the response variable (miles per gallon) for a one-unit increase in the explanatory variable (weight, in this case). Since the slope is negative (-1.4), it tells us that as weight increases, miles per gallon decreases. Specifically, for each additional one hundred pounds of weight, miles per gallon decreases by 1.4 miles.

question:Identify a situation that uses multiple regression. Which of the following situations describes a multiple regression? a.) Using IQ scores to predict the job performance of an individual. b.) Using the motivational level and the amount of social support to predict the job performance and IQ scores of an individual. c.) Using the motivation level, the amount of social support, and IQ scores to predict the job performance of an individual. d.) Using job performance to predict the motivational level and IQ scores of an individual.

answer:c.) Using the motivation level, the amount of social support, and IQ scores to predict the job performance of an individual. Multiple regression involves using two or more predictor variables to predict a response variable. In this case, motivation level, amount of social support, and IQ scores are all predictor variables that are being used to predict job performance, the response variable. Therefore, the situation described in option C involves multiple regression.

question:Calculate the value of a response variable using a least-squares line. By observing a set of data values, Thomas used a calculator for the weight (in pounds) and predicted the number of calories burned per minute to get an equation for the least-squares line: ŷ = 2.2 + 0.05x. Based on the information gathered by Thomas, select the statement that is TRUE. a.) A person weighing 149 pounds can burn 9.8 calories per minute. b.) A person weighing 134 pounds can burn 8.9 calories per minute. c.) A person weighing 173 pounds can burn 10.7 calories per minute. d.) A person weighing 125 pounds can burn 8.3 calories per minute.

answer:c.) A person weighing 173 pounds can burn 10.7 calories per minute. To calculate the predicted value of the response variable (calories burned per minute) for a given value of the explanatory variable (weight), we can substitute the weight value into the equation for the least-squares line and solve for ŷ. For example, to find the predicted calories burned per minute for a person weighing 173 pounds: ŷ = 2.2 + 0.05(173) ŷ = 2.2 + 8.65 ŷ = 10.85 Therefore, a person weighing 173 pounds can burn approximately 10.7 calories per minute (rounded to the nearest tenth). Using the same method, we can see that none of the other options are correct: a.) For a person weighing 149 pounds, ŷ = 9.15 b.) For a person weighing 134 pounds, ŷ = 8.0 d.) For a person weighing 125 pounds, ŷ = 7.75 Thus, option c is the only accurate statement.