# hw8 - Which value ofr indicates a stronger correlation r...

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Unformatted text preview: Which value ofr indicates a stronger correlation: r = -U.4SS or r = 0.554? Choose the value ofr with the stronger correlation. O 3- r = -D.4SS has a stronger correlation. Compare the values ofr in terms of their distances from CI. The value ofr with ‘5} b- r = 0.554 has a stronger correlation. the larger distance has the stronger correlation. Which of the values could not represent a correlation coefﬁcient? Choose the value that could not represent a correlation coefﬁcient. 1. 1923 Correlation coefﬁcients must be contained in the interval [-1, 1]. Choose the value that is not contained in this interval. The scatter plot ofpaired data sets is shown. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation between the variables. Which correlation best describes the scatter plot? O a. A negative linearcorrelation Ob. - . . . . . . . . N” 1”“ cmemm‘ Determine if there is a positive correlation, a negative correlation, or no (a C- A positive linear correlation CDHElEllCIﬂ. The scatter plot shows the results ofa survey of 18 selected males aged 22-35. Using age as the explanatory variable, choose the description of the scatter plot. Which description best describes the scatter plot? 0 a. Age and student loan balance [in thousands] O b. Age and income [in thousands] Look at the units of the vertical axis. For which of the three factors would you © 0 Age and heightmmches] expect the values to have a correlation such as displayed in the scatter plot?I Identify the explanatory variable and the response variable. A science student is taking temperatures measured in Fahrenheit and converting to temperatures measured in Celsius Choose the description that best categorizes the variables Degrees Celsius is the explanatory variable, and degrees Fahrenheit is the response variable. Think of the explanatory variable as the independent variable and the response Degrees Fahrenheit is the explanatory variable, and degrees Celsius is the response - hle as the dep endent . ble- variable. Display the data in a scatter plot. Calculate the linear correlation coefﬁcient I. Use the scatterplot to make a conclusion about the type of correlation. is D 1 2 3 4 y D. 5 3 2 4 3. 5 Find the correlation coefﬁcient. w= (Round to the nearest thousandth.) n 2 KY - [E r] [‘2 y] Choose the statement suggested by the scatter plot and the correlation coefﬁcient. Use the fﬂmnﬂa y = , where n is the nExQ—[ExF 312;}? —[E_;v]2 number of pairs of data. 0 b- There is a negative linear correlation. Alternatively, use the LinReg function on a graphing calculator. Look at the scatter plot and determine if the correlation is positive or negative. @ 8- There is a positive linear correlation. The data is from a study of the correlation between horsepower (hp) and expected gas mileage (mpg) for several vehicles. Find a critical value using a table value or technology to make a conclusion regarding the correlation coefficient. Use a = 0.01. hp 192 184 126 162 156 150 142 130 120 102 mpg 19 30 23 20 12 22 23 30 20 26 Find the correlation between horsepower and miles per gallon. r as -0. 121 (Round to the nearest thousandth.) Choose the correct statement. {.3 8 There is not enough evidence at the 1% level to conclude there is a significant linear I correlation. Miss—[2346?] Use technology or the formula I = 2 2 , where O b There is enough evidence at the 1% level to conclude there is a significant linear N' ’1 2X2 _ [EX] \l ’1 Eye _ [E y] correlation. n is the number ofpairs of data. Use atable to ﬁnd the critical value ofa data set with :1 =10 and CE = 0.01. Compare the absolute value of the correlation coefﬁcient to the critical value. If |r| > the critical value, the linear correlation is signiﬁcant. Identify the symbol or description for the term listed below. Regression line Choose the symbol or description which matches the above term. ('2' a. The line of best ﬁt 0 13- The difference between an observed y-value of a data point and the predicted x—value Review the definitions of the terms. Identify the correct symbol or description for the term listed below. The y-value of a data point corresponding to x:- Choose the symbol or description which matches the above term. Review the deﬁnitions ofthe terms. Match the graph of the regression equation to the regression equation. GRE math scores ..||..| |I.||I. X 50 “IUD 150 200 250 .300 350 400 Amount spent on test preparation (in dollars) Choose the regression equation that matches the graph of the data. 0 a. y =465.332x+ 0.5331 0 b. j» = 0.53312: - 465.332 The slope of the graph is either positive or negative and they-intercept is either 0 C. E = 05331): - 465.332 ('3 d. j.) = 0.53312: + 465.332 positive or negative. Test Grades Match the graph with the appropriate regression equation. Test grade 1D 12 14 15 Number of absences Select the regression equation that corresponds to the graph. 0 a. j; =4.?994x+93.4912 O b. j: = 49994:; - 93.4912 I _ I _ _ The constant is they-intercept, and the coefﬁc1ent IS the slope of the linear '3 c. 3’ = 93.49122: — 4.?99 {59 d. 3’ = -4.?994x+ 93.4912 regression equation Find the equation of the regression line for the given data. Then use the regression equation to predict the value of y for the given r-value, if meaningful. The age and the percentage of a certain medical procedure used is displayed. Age, (is) D 5 13 15 2D 25 33 Percentage, 0:) 16.5 16.3 12.3 13.2 13.5 13.9 21.2 Determine the regression equation. Use 1' for the predictor variable. y = D.14x+16.24 (Round the coefﬁcient and constant to the nearest hundredth.) Use the above equation for the regression line to predict they-value for x = 35, if meaningful. Oa. 325252114 09. 395311.34 Q d. It is not meaningful to predict the y-value for 3: =35. The equation ofa regression line is E’ = mx + b, where ,T’ is the predicted —value for a given x-value. The slope In and they-intercept b are given by HEIf—[EINEJ’] Hindi—[Ear]2 andb—F-mr — m— Whﬁfﬁ F is thﬁ 1106311 ofthey-values and f is the mean ofthe I—valucs. First, determine if it is meaningful to predict they-value for I = 35. Then, if it Alternatively, use the LinReg function on a graphing calculator. is, substitute 35 for x in the regression equation. Find the equation of the regression 1ine for the given data Then use the regression equation to predict the value ofy for the given x-value, if meaningful. x1223334456 y5463524656 Determine the regreSSion equation. Use x for the independent variable. y = U.13x+4.66 (Round the constant and the coefﬁcient to the nearest hundredth.) Use the above regreSSion equation to predict the value ofy for r = 6. @a- is: 544 Oh. is: 23.39 It is not meaningful to predict the value 0c. “ 333 0d. "1m ofy forx=6. The equation ofa regression line is y = IIIX + b , where J“? is the predicted y-value for a given x-value. The slope m and they—intercept b are given by HEW—[Erwin M 1m? 2.? megs—[2x]: an "y ' r1 m— where f is the mean ofmey-values and f is the mean ofthe x-valuea First, determine ifx = 6 is inside the range of the original data. Ifit is, then substitute 6 for x in the regression equation, using the rounded values. Evaluate Alternatively, use the LinReg function on a graphing calculator. the expression. Find the equation ofthe regression line for the given data. Then use the regression equation to predict the value of y for the given value of x, if meaningful. as 3.5 4.5 6.0 TS 10.0 15.0 y ?.0 ?.5 8.1 8.8 8.9 9.1 Determine the regression equation. Use x for the independent variable. y = 0.2x+ 6.9 (Round the constant and the coefﬁcient to the nearest tenth.) Use the rounded values of the regression equation to predict the y-value for x = 5. @a. yang Ob. 32:35.9 0 d It is not meaningful to predict the value Oc. " “v” 34'? ofy forx=5. The equation of a regression line is j‘ = mx + b , where 3) is the predicted y-value for a given x-value. The slope in and the y-intercept b are given by nExy-[EIJEEy] use—[2x]: andb=y_m m: where f is the mean of they-values and f is the mean of the x-values. Since I = 5 is in the range of the original data, it is meaningful to predict the Alternatively, use the LinReg function on a graph'ng calculator. value I3f}, for I = 5' Use the value of the correlation coefﬁcient to ca.culate the coefficient of determination. r= 0.460 Tind the coefﬁcient of determination. 0.2116 (Round to four decimal places.) What percentage of the variation of the data about the regression line is explained? a (Type an integer or a decimal.) What percentage ofthe variation ofthe data about the regression line is unexplained? (Type an integer or a decimal.) The coefﬁcient of determination is r2 . The sum of the explained variation and the unexplained variation is 100%. Use the value of the correlation coefﬁcient to calculate the coefﬁcient of determination. Find the percent of explained and unexplained variation. Express )3 as a percent. r= -0.606 :ind the coefﬁcient of determination. 0. 3672 (Round to four decimal places.) What percentage of the variation of the data ab out the regression line is explained? 36.?2 |% (Round to the nearest hundredth.) What percentage of the variation of the data ab out the regression line is unexplained? 63.23 |% (Round to the nearest hundredth) The coefﬁcient of determination is r2 . The sum of the explained variation and the unexplained variation is 100%. Use the data to ﬁnd the coefficient of determination and the standard error of estimate Se. x 1 2 3 4 5 6 y 2.5 3.9 4.3 5 5.2 6.3 The equation ofthe regression line is it = 8.212143 r+ 2.18662. Find the coefﬁcient of determination. r2= (Round to the nearest thousandth.) Find the total variation and the explained variation and find the ratio of the two Find the standard error of estimate. values. (Round to the nearest thousandth.) E 12’: — F] The table shows median weekly earnings (in US. dollars) of full-time male and female workers for five years. The equation ofthe regression line is j? = 8.596219 x+125.684. Medianweeklyeamjngsofmaleworkersm 629 622 618 552 649 Medianmeklyeanﬁngsoffemalemrkers,y 592 529 511 423 418 Find the coefﬁcient of determination. )3 = 8.21 (Round to the nearest thousandth.) Use the formula for the standard error of estimate. Find the standard mm of 65mm- 5 _ E D’s-fr]; 5.; = 66.426 '3 _ n _ 2 (Round to the nearest thousandth.) First find the explained variation and the total variation. Then use the definition ofthe coefficient of determination. Use the formulas. Explained variation = 2 m — \$12 Total . mm = E U)! _mg Use the formula for the standard error of estimate. r2 _ Explained variation 2 E (y:- — fl)? — + 59 = — Total variation ,4 _ 2 Use the multiple regression equation to predict the y-values for the given values of the independent variables. J2 = 6682 + 31.8I1 - 8.58930 Predict they-value when in = 1562 and I; = 1483. 55639113 Substitute the values for x1 and X; into the equation and simplify the (Round to the nearest thousandth.) expression. .iple regression equation to predict the y-values for the given values of the independent 3‘ =8.123+ 8.213x1 + 8.84412 Predict they-value for in = 36 and I: = 12. 16.319 (Round to the nearest thousandth.) Substitute the values into the regression equation, and simplify. The partial computer Predietor Coef SE Coef T display gives the results of Intercept 9.829 8.299 18.662 amultiple regression analysis. X1 8.123 8.822 5.228 Use the display to determine X2 8.851 8.841 1.221 the equation, the standard error of estimate, and the coefﬁcient S = 8.324 R-sq = 88.1% R-sq(adj) =98.2% of determination. Choose the correct regression equation. @3- J2 =9.829+ 8.1231'1+8.8511'2 09- :1" =9.829l'1+8.12312 + 8.851 What is the standard error of estimate? Se = 8.324 (Type a decimal. Do not round.) The "Coef" column contains the equation coefficients. Be sure to assign the What is the coefficient of determination? 8.881 (Type a decimal. Do not round.) correct values to the correct coefﬁcients. The partial computer Predictor display gives the results of Intercept a multiple regression analysis. X1 Use the display to determine X2 the equation, the standard error of estimate, and the coefﬁcient S = 0.416 of determination. Choose the correct regression equation. @a. j} =3.123+U.213x1+ﬂ.ﬂ44m What is the standard error of estimate? .5,3 = What is the coefﬁcient of determination? The standard error of estimate is given in the computer display as "S". Coef 3.123 0.213 0.044 R-sq = 83.1% Ob. 0.416 0.331 (Type a decimal. Do not round.) The standard error of estimate is given in the computer display as "S". Convert the value for R-sq in the computer display from a percentage to a decimal. T 13.66? 5.228 1.??‘1 SE Coef 0.299 0.022 0.041 R-sq(adj) =90. 2% 3’ = 8.12311 + 02133:: + 0.044 (Type a decimal. Do not round.) The "Coef" column contains the equation coefﬁcients. Be sure to assign the correct values to the correct coefﬁcients. Convert the value for R-sq in the computer display from a percentage to a decimal. ...
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## This note was uploaded on 04/01/2012 for the course MGQ 301 taught by Professor Orrange during the Fall '09 term at SUNY Buffalo.

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hw8 - Which value ofr indicates a stronger correlation r...

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