Question 1

Use the following information for questions: A regression was done for 20 cities with latitude as the explanatory variable (x) and average January temperature as the response variable (y). The latitude is measured in degrees and average January temperature in degrees Fahrenheit. The latitudes ranged from 26 (Miami) to 47 (Duluth) The regression equation is $\hat{y}$ = 49.4 - 0.313x. -The total sum of squares (SSTO) = 4436.6, and the error sum of squares (SSE) = 1185.8. What is the value of r² the proportion of variation in y explained by its linear relationship with x?

Accepted Answer

The answer of Use the following information for questions:
 A...

Question 2

Use the following information for questions:
 A regression was done for 20 cities with latitude as the explanatory variable (x) and average January temperature as the response variable (y). The latitude is measured in degrees and average January temperature in degrees Fahrenheit. The latitudes ranged from 26 (Miami) to 47 (Duluth) The regression equation is $\hat{y}$ = 49.4 - 0.313x.
-What is the value of the correlation coefficient r?

Accepted Answer

The answer of Use the following information for questions:
 A...

Question 3

A counselor at a weight-loss clinic wishes to determine if there is a relationship between BMI and depression. The scores of 6 patients are determined. She makes a scatterplot to assess of the relationship appears to be linear. It turns out to be a positive linear relationship. The Sum of Squared Errors is 8.875 and the Total Sum of Squares (SSTO) is 17.5. What is the value of the correlation coefficient between BMI and depression?

Accepted Answer

The answer of A counselor at a weight-loss clinic wishes...

Question 4

A psychology student wishes to determine the strength of the relationship between school grades and short term memory. Twenty-two students were given a memory test. SPSS was used to analyze the data. Part of the output is shown below. 
   What is the value of the correlation coefficient between grades and the memory test scores?

Accepted Answer

The answer of A psychology student wishes to determine the...

Question 5

A scatterplot of the self-reported weights (y variable) and self-reported heights (x variable) for 176 college students follows.  What is the main difficulty with using a regression line to analyze these data?

Accepted Answer

The answer of A scatterplot of the self-reported weights (y...

Question 6

A scatterplot of the price of a book (y variable) versus the number of pages in the book (x variable) is shown for 15 books in a professors office. In addition, the symbol "o" shows that the book was a hardcover book, while the symbol "+" shows that the book was a softcover book.  What is the main difficulty with using a regression line to analyze these data?

Accepted Answer

The answer of A scatterplot of the price of a...

Question 7

A researcher would like to study the relationship between y = graduating GPA of students at a university and x = major field of study (1 = science, 2 = humanities, etc.). What is a possible difficulty with using a regression line to analyze these data?

Accepted Answer

The explanatory variable (major field of study) is categorical, not quantitative, which makes it inappropriate for analysis using a regression line that assumes a quantitative relationship between variables.

Question 8

Based on 1988 census data for the 50 States in the United States, the correlation between the number of churches per state and the number of violent crimes per state was 0.85. What can we conclude?

Accepted Answer

The correlation of 0.85 between the number of churches per state and the number of violent crimes per state does not imply causation. Instead, it suggests that both variables are likely related to a third variable, which is the population size of the state. Larger populations tend to have more churches and also report more violent crimes, making population size a confounding variable that explains the observed correlation.

Question 9

What is the effect of an outlier on the value of a correlation coefficient?

Accepted Answer

Outliers can have a significant impact on the value of a correlation coefficient, potentially increasing or decreasing it depending on their position relative to the main data cluster. Their effect is not uniform and depends on their location in the dataset.

Question 10

A scatter plot of number of teachers and number of people with college degrees for cities in Pennsylvania reveals a positive association. The most likely explanation for this positive association is:

Accepted Answer

Larger cities naturally have more people, which leads to both more teachers and more people with college degrees, explaining the positive association.

Question 11

Use the following information for questions:
 Consider the following scatterplots for two quantitative variables y and x. One point has been labeled in each plot.
 
-Which point would be the most influential?

Accepted Answer

Point B would be the most influential because it is likely positioned far from the main cluster of data, having a greater impact on the slope and intercept of a regression line. Influential points are typically outliers in the x direction, significantly affecting the model's predictions.

Question 12

Use the following information for questions:
 Consider the following scatterplots for two quantitative variables y and x. One point has been labeled in each plot.
 
-Which point would produce the largest residual?

Accepted Answer

Point A is the furthest point from the line of best fit, so it would produce the largest residual.

Question 13

A professor found a negative correlation between the number of hours students came to her office hours and their score on her final exam. What possible confounding variable could explain the observed negative correlation?

Accepted Answer

The answer of A professor found a negative correlation between...

Question 14

Suppose a study of employees at a large company found a negative correlation between weight and distance walked on an average day. Explain why a conclusion that walking reduces weight cannot be made from this study (i.e. What confounding variable could also explain the observed negative correlation?)

Accepted Answer

The answer of Suppose a study of employees at a...

Question 15

A survey of students found a negative correlation between the weekly hours of T.V. watched and the weekly hours spent exercising. One student explained that reducing the hours of T.V. watched (cause) would result in students sleeping longer and having more energy to exercise (effect). Give another explanation with hours of exercise as the cause and hours T.V. watched as the effect.

Accepted Answer

The answer of A survey of students found a negative...

Question 16

A researcher found a positive correlation between the number of hours elementary school children spend watching T.V. (weekly) and their reading score on a standardized exam. What possible confounding variable could explain the observed positive correlation?

Accepted Answer

The answer of A researcher found a positive correlation between...

Question 17

The scatterplot below shows student heights (y axis) versus father's heights (x axis) for a sample of 173 college students. The symbol "+" represents a male student and the symbol "o" is represents a female student.
  Based on the scatterplot, what is the problem with using a regression equation for all 173 students?

Accepted Answer

The answer of The scatterplot below shows student heights (y...

Question 18

What are influential observations and where are they generally found?

Accepted Answer

The answer of What are influential observations and where are...

Question 19

The 25 item "Parenting Hassles Scale" asks parents questions about certain situations in their family. They are asked to rate these situations on (1) how often they occur (frequency), and (2) how much they bother them (intensity). The score system for the frequency was 0-4 points (0 = never, 4 = all the time) and for the intensity 1-5 (1 = not much at all, 5 = very much). If an item received a 0 (zero) for frequency, it automatically received a 0 (zero) for intensity. The two variables, frequency and intensity, were formed by taking the total of the corresponding scores from the two rating scales across the various situations These two variables are then used to create a scatterplot. The symbols indicate whether a mother, a father, or a step parent filled in the questionnaire.
  Based on the scatterplot, what is the problem with using one regression equation for all parents combined?

Accepted Answer

The answer of The 25 item "Parenting Hassles Scale" asks...

Quiz 3: Relationships Between Quantitative Variables

A scatterplot of the self-reported weights (y variable) and self-reported heights (x variable) for 176 college students follows. What is the main difficulty with using a regression line to analyze these data?

A researcher would like to study the relationship between y = graduating GPA of students at a university and x = major field of study (1 = science, 2 = humanities, etc.) . What is a possible difficulty with using a regression line to analyze these data?