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Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases? Choose the correct answer below. O The dependent variable decreases. O The dependent variable increases.Which value of r indicates a stronger correlation: r= 0.715 or r= - 0.897? Explain your reasoning. Choose the correct answer below. O A. = 0.715 represents a stronger correlation because 0.715 > - 0.897. O B. r= 0.715 represents a stronger correlation because | - 0.897 | > |0.715). O C. r= - 0.897 represents a stronger correlation because | - 0.897 | > |0.715). O D. r= - 0.897 represents a stronger correlation because 0.715> -0.897.Choose the correct answer below. 0 A. Two variables that have perfect positive linear correlation are the price per gallon of gasoline and the total cost of gasoline. Two variables that have perfect negative linear correlation are the distance from a door and the height at a wheelchair ramp. 0 B. Two variables that have perfect positive linear correlation are the price per gallon of gasoline and the height of a wheelchair ramp. Two variables that have perfect negative llnear correlation are the distance from a door and the total cost of gasoline. O 6. Two variables that have perfect pcsilive linear correlation are the distance from the door and the height of a wheelchair ramp. Two variables that have perfect negative linear correlation are the price per gallon ofgasoline and the total cost of gasoline. O D. Two variables that have perfect positive linear correlation are the total cost of weekly groceries and the total costof gasoline. Two variables that have perfect negative linear correlation are the distance from a door and the number of steps toget through the door. For each of the scatter plots below, determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables. . Drag each of the scatter plots given above into the appropriate area below. perfect positive linear correlation strong positive linear correlation perfect negative linear correlation strong negative linear correlation no linear correlationIdentify the explanatory variable and the response variable. A golfer wants to determine if the number of lessons received every year can be used to predict the amount of improvement in his game. The explanatory variable is the The response variable is the number of lessons amount of improvement in his game golferThe accompanying table shows the height (in inches] of 8 high school girls and their scores on an IQ test. Complete parts (a) through {d} below. Click here to View the data table. Click here to View the table of critical values for the Pearson correlation coefcient. I'T\" {a} Display the date in a scatter plot. Choose the correct graph below. 0 A. O B. O c. O D. A A A 72:33:33]: 6' 13\" Q 72' Q g 33 a g '2\" ' a g 3 9. HIDIla c 50 a e a 50 ' 5e . ct ' we - ct ' 5e :4 52 ) 90 ' ) 52 ) 90 i ) W 1" D 52 72 W 1"I] 52 72 Height nches] Height (Inches) Height nches] Height nches] Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative\"? C} A. The slope is negative. As the independent variable increases the dependent variable tends to decrease. O B. The slope is negative. As the independent variable increases the dependent variable also tends to increase. 0 G. The slope is positive. As the independent variable increases the dependent variable tends to decrease. O D. The slope is positive. As the independent variable increases the dependent variable also tends to increase. In order to predict y-values using the equation of a regression line, what must be true about the correlation coefficient of the variables? Choose the correct answer below. O A. The correlation between variables must be significant. O B. The correlation between variables must be greater than zero. O C. The correlation between variables must be a y-value of a point on the graph. O D. The correlation between variables must be an x-value of a point on the graph.Drag each graph given below to its corresponding regression equation to the right. 30- 13. y = - 1.361x +21.952 25- 30- 20- 25- 15 20- 10 15 5. 10- 5- N- 6 8 10 5 10 15 20 25 30 35 40 Ay 14. y = 2.115x + 21.958 70- O Ay 60- 140- 50- 120- 40- 100 30- 80- 20- 60- 10 . . . . . 40- 20- 5 10 15 20 25 30 10 20 30 40 50 15. y = 2.125x + 9.588 16. y = - 0.705x + 27.214Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below. Hours spent studying, x 0 1 3 3 4 5 (a) x = 2 hours Test score, y 39 44 (b) x =4.5 hours 52 48 61 68 (c) x = 14 hours (d) x = 3.5 hours Find the regression equation. y=* + (0) (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.)Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? r= - 0.553 Calculate the coefficient of determination. (Round to three decimal places as needed.)Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? r= - 0.961 Calculate the coefficient of determination. (Round to three decimal places as needed.)