Select all the statements that are true of a least-squares regression line. R measures how much of the variation in Y is explained by X in the estimated linear regression. The regression line is used to predict nonlinear patterns. In the equation of the least-squares regression line, Y is a predicted value when X is known. The slope of the regression line is resistant to outliers. The sum of the squares of the residuals is the smallest sum possible. In the equation of the least-squares regression line, Ý is an observed value when X is known.

the scatter plot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. the equation of the line y=-14.7+1.59x is called the least-squares regression line because it

We have data on Lung Capacity of persons and we wish to build a multiple linear regression model that predicts Lung Capacity based on the predictors Age and Smoking Status. Age is a numeric variable whereas Smoke is a categorical variable (0 if non-smoker, 1 if smoker). Here is the partial result from STATISTICA. b* Std.Err. of b* Std.Err. N=725 of b Intercept Age Smoke 0.835543 -0.075120 1.085725 0.555396 0.182989 0.014378 0.021631 0.021631 -0.648588 0.186761 Which of the following statements is absolutely false? A. The expected lung capacity of a smoker is expected to be 0.648588 lower than that of a non-smoker. B. The predictor variables Age and Smoker both contribute significantly to the model. C. For every one year that a person gets older, the lung capacity is expected to increase by 0.555396 units, holding smoker status constant. D. For every one unit increase in smoker status, lung capacity is expected to decrease by 0.648588 units, holding age constant.

A professor was doing a study on the relationship between the amount of television a person watches per day (in hours) and the person's IQ. The professor found that a linear relationship exists between the two variables and determined the equation of the least squares regression line to be ŷ = -0.4x + 107. Interpret the slope. [ Select ] ( Select ] As a person's IQ increases by 1 point, the amount the person spends watching television increases by 0.4 hours, on average. As a person's IQ increases by 1 point, the amount the person spends watching television decreases by 0.4 hours, on average. As the amount of time a person watches TV increases by 1 hour, the person's IQ is expected to increase by 0.4 points, on average. As the amount of time a person watches TV increases by 1 hour, the person's IQ is expected to decrease by 0.4 points, on average. Predict the IQ of a person who watches 3 hours of television per day. [ Select] Dexter spends 4 hours watching television per day and has an…

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.)

Tire pressure (psi) and mileage (mpg) were recorded for a random sample of seven cars of thesame make and model. The extended data table (left) and fit model report (right) are based on aquadratic model. Calculate R2. Describe what this value means in the context of the problem.

A simple linear regression that describes the effect of individuals’ cigarette smoking on health is given by Health = α + β * cigarettes + u, where Health is a measure of health that is on the scale of 1 to 5, where 1 means excellent health and 5 means poor health. So the bigger the number, the worse the health. cigarettes is the average number of cigarettes smoked per day; the unobservable u is an individual’s health consciousness. Note that health conscious person tends to live a healthy life in general.   What will happen to β if cigarettes is in terms of weekly rather than daily?

The table below shows the amounts of crude oil (in thousands of barrels per day) produced by a country and the amounts of crude oil (in thousands of barrels per day) imported by a country, for the last seven years. Construct and interpret a 98% prediction interval for the amount of crude oil imported by the this country when the amount of crude oil produced by the country is 5,583 thousand barrels per day. The equation of the regression line is V = - 1.116x + 15,810.670. Oil produced, x Oil imported, y 5,773 5,694 5,638 5,481 5,165 5,051 5,010 9,345 9,132 9,616 10,049 10,152 10,165 10,030 Construct and interpret a 98% prediction interval for the amount of crude oil imported when the amount of crude oil produced by the country is 5,583 thousand barrels per day. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest cent as needed.) O A. There is a 98% chance that the predicted amount of oil imported is between and thousand barrels,…

Suppose a new point was added to your data: a wine that is 20% alcohol that contains 0calories. How will that affect the value of r and the slope of the regression line? (Nocalculation needed)

Draw a graph of the least-squares regression line on your scatterplot. (For hand-drawing, round the slope and y-intercept to one decimal place before drawing the line.) Be sure to show how you were able to plot the line starting with its equation. Model City Miles per Gallon Highway Miles per Gallon Acura RLX 20 29 BMW 530i 24 34 Buick LaCrosse eAssist 25 35 Chevrolet Malibu 29 36 Ford Hybrid FWD 43 41 Honda Civic 32 42 Infiniti Q50 Red Sport 20 26 Kia Forte 30 40 Lexus ES 350 22 33 Mercedes Benz AMG S 21 30 Mini Cooper Clubman 24 32 Nissan Maxima 20 30 Suburu Legacy AWD 25 34 Toyota Prius ECO 58 53