Given are five observations for two variables, and y. 42 4 14 18 20 | S7 4 14 10 Ue the estimated regression equation is-67.-263e. a. Compute the mean square error using equation - MSE - SSE ea decima) b. Compute the standard eror of the estimate using equation. SSE VSESE (to 2 decima) e. Compute the estimated standard deviation of using equation.
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- Given below are five observations collected in a regression study on two variables x (independent variable) and y (dependent variable). X Y 10 7 20 5 30 4 40 2 50 1 a. Develop the least squares estimated regression equation. b. At the 5% level of significance, perform a t test and determine whether or not the slope is significantly different from zero. d. Compute the coefficient of determination. e. Compute the coefficient of correlation.The marketing manager of a supermarket chain would like to determine the effect of shelf spaceon the sales of pet food. A random sample of 10 stores was selected, and the results are presentedbelow. Store shelf space in cm weekly sales in thousand pesos 1 45 18 2 45 21 3 75 15 4 80 18 5 95 23 6 100 26 7 135 22 8 140 27 9 185 25 10 190 28 d. Using the estimated simple linear regression equation Y=15.6414+0.0611X, estimate the weekly sales when theshelf space is 230cm? 250cm? e. Compute the coefficient of determination and interpret its value.The table below shows the average weekly wages (in dollars) for state government employees and federal government employees for 10 years. Construct and interpret a 95% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $841. The equation of the regression line is ModifyingAbove .y=1.403x+9.259. Wages (state), x 724 747 800 803 839 897 901 939 951 956 Wages (federal), y 1,035 1,060 1,111 1,144 1,190 1,245 1,276 1,306 1,332 1,396 Construct and interpret a 95% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $841. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest cent as needed.) A. There is a 95% chance that the predicted average weekly wages of federal government…
- Here is a bivariate data set. Find the regression equation for the response variable y. x y 36.6 56.9 34.9 51.8 24.2 65.9 36.3 61 23.6 65.6 40.3 63.3 8.1 63.3 39.9 52.2 38.6 61.4 43.1 51.2 regression equation: ? Enter the equation in slope-intercept form with parameters accurate to three decimal places.Given below are five observations collected in a regression study on two variables, x (independent variable) and y (dependent variable).x y2 43 44 35 26 1a. Develop the least squares estimated regression equation.b. Compute the coefficient of determination.c. Compute the coefficient of correlation.The following data represent the number of calculators sold per day at a retail shop and their prices. You must do the following by hand and show all of your work: Price (x) Units Sold (y) 71 3 50 4 37 6 10 5 21 9 76 2 43 1 Develop a least-squares regression line and interpret the coefficient on x. Compute R-squared and comment on the strength of the relationship between x and y. Determine the statistical significance of the coefficient estimate using both an F test and a t-test. Use alpha=0.05.
- Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2 The least-squares estimate of b0 equals [2 decimal points] ________ The least squares estimate of b1 equals [2 decimal points; also don't forget the sign] __________ Develop the least squares estimated regression equation _______ At 95% confidence, perform a t test and determine whether the slope is significantly different from zero. [3 decimals] t = _____________ Based on this information, we Reject H0 Do not reject H0 The coefficient of determination is [keep 3 decimal points] _________A statistics professor wants to determine how students' final grades are related to mid-term exam scores, applied in the middle of the term, and the number of classes missed. The teacher selects 10 students from his class and obtains the following data as an attachment. Y = b + m1x1 + m2x2 being the general form of the multiple regression equation referring to the data above. Check the alternative that corresponds to the approximate value of b, m1 and m2, respectively: a) 46,39; 0,54; -4,89 b) -4,89; 0,54; 46,39 c) 46,39; -4,89; 0,54 d) -4,89; 46,39; 0,54The article “Models for Assessing Hoisting Times of Tower Cranes” (A. Leung and C. Tam, Journal of Construction Engineering and Management, 1999: 385–391) presents a model constructed by a stepwise regression procedure to predict the time needed for a tower crane hoisting operation. Twenty variables were considered, and the stepwise procedure chose a nine-variable model. The adjusted R2 for the selected model was 0.73. True or false: a) The value 0.73 is a reliable measure of the goodness of fit of the selected model. b) The value 0.73 may exaggerate the goodness of fit of the model. c) A stepwise regression procedure selects only variables that are of some use in predicting the value of the dependent variable. d) It is possible for a variable that is of no use in predicting the value of a dependent variable to be part of a model selected by a stepwise regression procedure.
- A researcher is proposing that exercise makes a person more energized as a result they require less sleep. He carries out a survey on the number of hours of exercise per week and the average hours of sleep needed per night in order to feel well rested. The results are shown on page 2 for the 8 participants. Calculate and interpret the regression line for the data. Hours of exercise/week (x) Average hours of sleep needed/night (Y) 8.6 4 8.1 5.2 9 2 8.5 3.4 7.4 8 6.8 10 9.4 1.5 7.7 6Which of the following best describes a regression coefficient in a bivariate setting? a. The change in Y predicted by a unit change in X b. The slope of a line that minimizes the sum of squared residuals c. The correlation coefficient multiplied by SDy/SDx d. All of the aboveUsing the regression line attached. Based on only the above plot, one can conclude: a) height causes an increase in weight b) weight causes an increase in height c) taller people are more likely to weigh more than shorter people, at least in the sample on which this data is based d) a statistically significant predictive relationship between height and weight e) c and d