Suppose that a multiple linear regression model was fit to data and that the following output resulted: Coefficients: (Intercept) stop distance mpg weight Estimate 8.63315 -0.06078  -0.03793 0.17295 Std. Error 5.91641 0.07368 0.08661 0.08165 t value 1.459 -0.825  -0.438  2.118 Pr(>|t|) 0.1482 0.4117 0.6626 0.0371 True or False? It is likely that at least one explanatory variable would be left in our model if a backwards selection process were performed. (Our significance level is 0.05 for all testing purposes.)  True False

Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. Explain clearly what this slope says about the change in the mean of y for a change in x.

The flow rate in a device used for air quality measurement depends on the pressure drop x (inches of water) across the device's filter. Suppose that for x values between 5 and 20, these two variables are related according to the simple linear regression model with true regression line y = -0.11 + 0.097x. (a.1) What is the true average flow rate for a pressure drop of 10 in.?(a.2) A drop of 15 in.?(b) What is the true average change in flow rate associated with a 1 inch increase in pressure drop?(c) What is the average change in flow rate when pressure drop decreases by 5 in.?

A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.5+ 14.4x Coefficients (Intercept) x Estimate 4.5 Ho: B₁ = 0 H₁: B₁ > 0 Ho: B₁ = 0 Ha: B₁ <0 14.4 Ho: B₁ = 0 Ha: B₁ #0 Std. Error Test statistic 2.9 4.7 1.55 3.06 P-value Specify the null and the alternative hypotheses that you would use in order to test whether a linear relationship exists between x and y. 0.07 0

If the R-squared for a regression model relating the outcome y to an explanatory variable x is 0.9. This implies that there is a positive linear relationship between y and x. True or false?

A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x₁ = distance traveled (miles) and x₂ = the number of deliveries made. Suppose that the model equation is Y = -0.800+ 0.060x₁ +0.900x₂ + e (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? hr (b) How would you interpret ₁ = 0.060, the coefficient of the predictor x₁? O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a one-mile (i.e.…

The accompanying table shows results from regressions performed on data from a random sample of 21 cars. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). The equation CITY - 3.17 +0.823HWY was previously determined to be the best for predicting city fuel consumption. A car weighs 2700 lb, it has an engine displacement of 1.6 L, and its highway fuel consumption is 35 mi/gal. What is the best predicted value of the city fuel consumption? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate? Click the icon to view the table of regression equations. The best predicted value of the city fuel consumption is (Type an integer or a decimal. Do not round.). Regression Table I R² Adjusted R2 WT/DISP WT/HWY Predictor (x) Variables P-Value WT/DISP/HWY 0.000 0.942 0.000 0.748 0.000 0.942 0.000…

B b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? The scatter diagram indicates a positive linear relationship between a = average number of passing yar and y = the percentage of games won by the team. c. Develop the estimated regression equation that could be used to predict the percentage of games won given the avera passing yards per attempt. Enter negative value as negative number. WinPct =| |)(Yds/Att) (to 4 decimals) d. Provide an interpretation for the slope of the estimated regression equation (to 1 decimal). The slope of the estimated regression line is approximately So, for every increase : of one yar number of passes per attempt, the percentage of games won by the team increases by %. e. For the 2011 season, the average number of passing yards per attempt for the Kansas City Chiefs was was 5.5. Use th regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs.…