Statistics Module 2 (Questions and Answers A+ Graded 100% Verified)

Statistics Module 2 (Questions and Answers A+ Graded 100% Verified) Statistics Module 2 (Questions and Answers A+ Graded 100% Verified) Scatterplot Correct Answer: Used to summarize the relationship between two quantitative variables that have ben measured on the same element. When examining relationship between 2 quantitative variables, your best bet is to start with a scatterplot. Graph of points (x,y), each of which represents one observation from the data set Scatterplots provide a visual description of the relationship between two quantitative variables. X variable Correct Answer: Variable measured along horizontal axis. Y variable Correct Answer: Variable measured along vertical axis. Relationship between two quantitative variables can take many different forms: POSITIVE LINEAR RELATIONSHIP Correct Answer: As x increases, y also tends to increase. Relationship between two quantitative variables can take many different forms: NEGATIVE LINEAR RELATIONSHIP Correct Answer: As x increases, y tends to decrease. Relationship between two quantitative variables can take many different forms: NO CORRELATION/APPARENT RELATIONSHIP Correct Answer: As x increases, y tends to remain unchanged. Relationship between two quantitative variables can take many different forms: NONLINEAR RELATIONSHIP Correct Answer: The x and y variable are related, but not in a way that can be approximated using a straight line. Correct Answer: USING CALCULATOR TO GET SCATTERPLOT Correct Answer: Step 1: Enter the x variable (square footage) into L1 and the y variable (sales price) into L2. Step 2: Press 2nd, then Y= for the STAT PLOTS menu. Step 3: Select 1, and press ENTER. Select ON, and press ENTER. Step 4: Select the scatterplots icon and press ZOOM 9. Horizontal line on Scatterplot (x) Correct Answer: PREDICTOR VARIABLE input Vertical line on Scatterplot (y) Correct Answer: RESPONSE VARIABLE CORRELATION COEFFICIENT Correct Answer: A numerical measure for quantifying the linear relationship between two quantitative variables. Correlation coefficient r measures the strength and direction of the LINEAR RELATIONSHIP between two variables. The correlation coefficient r is where sx is the sample standard deviation of the x data values, and sy is the sample standard deviation of the y data values. CORRELATION COEFFICIENT R Correct Answer: --is always -1 ≤ r ≤ 1 (GREATER THAN NEGATIVE ONE AND LESS THAN ONE) --When r = +1, a perfect positive relationship exists between x and y. --When r = -1, a perfect negative relationship exists between x and y. --Values of r near 0 indicate there is no linear relationship between x and y. POSITIVE RELATIONSHIP/ASSOCIATION Correct Answer: Values of r near +1 The closer r gets to +1, the stronger the evidence for a positive relationship=variables positively associated. • As X INCREASES, Y tends to INCREASE. NEGATIVE RELATIONSHIP/ASSOCIATION Correct Answer: When r = -1, a perfect negative relationship exists between x and y. Values of r near -1 indicate a negative relationship between x and y. • The closer r gets to -1, the stronger the evidence for a negative relationship. • The variables are said to be negatively associated. • As X INCREASES, Y tends to DECREASES. NO ASSOCIATION/NONLINEARLY ASSOCIATED Correct Answer: Values of r near 0 indicate there is no linear relationship between x and y. • The CLOSER R GETS to 0, the WEAKER the evidence for a LINEAR RELATIONSHIP • The variables are not linearly associated. • A nonlinear relationship may exist between x and y. • Close to 0 DOES NOT IMPLY NO RELATION, just NO LINEAR RELATION. PERFECT POSITIVE RELATIONSHIP Correct Answer: r=+1 PERFECT NEGATIVE RELATIONSHIP Correct Answer: r=-1 r=0.9 Correct Answer: strong positive relationship between x and y r=-0.9 Correct Answer: strong negative relationship between x and y r=0.5 Correct Answer: weak positive relationship between x and y r=-0.5 Correct Answer: weak negative relationship between x and y r=0 Correct Answer: NO LINEAR RELATIONSHIP between x and y (NOT NO RELATIONSHIP...just no LINEAR RELATIONSHIP.) r=0 no linear relationship Correct Answer: Which of the following values is not an acceptable value for the correlation cofficient, r ? A. r=0.8 B. r=0 C. r=1 D. r=5 E. All of the above values are possible values for r. Correct Answer: D. r=5 R HAS TO BE BETWEEN -1 and 1. EQUATION OF THE REGRESSION LINE Correct Answer: yˆ = b1x + b0 B1=slope B0=Y intercept The "hat" over the y (pronounced "y-hat") indicates this is an ESTIMATE of y and not necessarily an ACTUAL VALUE of y. Y-hat Correct Answer: an ESTIMATE of Y. Not necessarily the actual value. SLOPE of the regression line Correct Answer: The estimated CHANGE in Y PER UNIT INCREASE in X. Y-Intercept Correct Answer: the ESTIMATED VALUE of Y when X = 0. slope and y-intercept Correct Answer: Equation of REGRESSION LINE Correct Answer: b1 is the slope b0 is the y-intercept SLOPE b1 and correlation coefficient r : Correct Answer: --ALWAYS HAVE THE SAME SIGN --b1 is positive if and only if r is positive --b2 is negative if and only if r is negative Can see sign of correlation from slope in the equation. USING CALCULATOR TO make scatterplot then FIND CORRELATION COEFFICIENT R AND REGRESSION EQUATION Correct Answer: STAT 1 Enter data into L1 and L2 (create scatterplot) 2nd y= 1 enter scroll to get type of graph you want zoom 9 STAT CALC 4:LinReg (ax+b) 2nd 1 , 2nd 2 ENTER X Y 110 52 120 55 130 58 140 56 150 59 Correct Answer: y=ax+b (a=slope; b=y-intercept) Compute slope: 0.150 r2 Correct Answer: IS BETWEEN 0 AND 1 SO IS ALWAYS POSITIVE MEASURES THE GOODNESS OF FIT OF THE REGRESSION EQUATION TO THE DATA