1. Which linear relationship has a stronger correlation, a relationship with r=−0.84 or a relationship with r=0.72? Explain. (1 point)
A. The linear relationship with r=0.72 because it has the smallest absolute value.
B. The linear relationship with r=0.72 because it is the closest to 1.
C. The linear relationship with r=−0.84 because it is the closest to −1.
D. The linear relationship with r=−0.84 because the absolute value of r is closer to 1.
2. A biology student is investigating the claim that the temperature can be predicted by counting cricket chirps. He collected some data and found that the correlation coefficient is 0.82. What kind of correlation exists between the variables? (1 point)
A. a strong negative correlation
B. a strong positive correlation
C. a weak positive correlation
D. a weak negative correlation
3. A researcher monitoring the power from the solar panels on a Mars lander has developed a regression model for the available power output in watts, P, against the number of days since landing, d, to help predict the change in power due to dust accumulation. The correlation coefficient is −0.92. What kind of correlation exists between the variables?
A. a weak positive correlation
B. a strong positive correlation
C. a weak negative correlation
D. a strong negative correlation
4. A real estate agent has developed a linear model for the price of a house, P, in dollars in terms of the area, A, in square feet for the homes in a certain neighborhood. The correlation coefficient for the relationship is 0.42. What kind of correlation exists between the variables? (1 point)
A. a strong positive correlation
B. a weak negative correlation
C. a weak positive correlation
D. a strong negative correlation
5. A fisherman has collected data about the length in inches, L, and weight in ounces, w, of fish he has caught. The data are in the table below. What is the correlation coefficient?
L 12 16 16 17 18 19 21 23
w 8 17 19 20 27 30 37 42
A. r=0.978
B. r=−33.274
C. r=3.283
D. r=0.989
please help
1. C. The linear relationship with r=−0.84 because it is the closest to −1, indicating a strong negative correlation.
2. B. A strong positive correlation exists between the variables.
3. D. A strong negative correlation exists between the variables.
4. C. A weak positive correlation exists between the variables.
5. D. r=0.989.
thx i got a 4/5
1. The linear relationship with a correlation coefficient of -0.84 has a stronger correlation. Option C is the correct answer. A correlation coefficient ranges from -1 to +1, with values closer to -1 or +1 indicating a stronger correlation. In this case, -0.84 is closer to -1 than 0.72 is to 1, indicating a stronger negative correlation.
2. The correlation coefficient of 0.82 indicates a strong positive correlation between the variables. Option B is the correct answer. A correlation coefficient between 0.7 and 1 indicates a strong positive correlation, meaning that as the number of cricket chirps increases, the temperature also increases.
3. The correlation coefficient of -0.92 indicates a strong negative correlation between the variables. Option D is the correct answer. A correlation coefficient between -0.7 and -1 indicates a strong negative correlation, suggesting that as the number of days since landing increases, the power output from the solar panels decreases due to dust accumulation.
4. The correlation coefficient of 0.42 indicates a weak positive correlation between the variables. Option C is the correct answer. A correlation coefficient between 0 and 0.3 indicates a weak positive correlation, suggesting that as the area of the house increases, the price also tends to increase but the relationship is not very strong.
5. To find the correlation coefficient for the given data, we can use the formula:
r = [Σ((L - L̅)(w - w̅))] / [√(Σ(L - L̅)^2) * √(Σ(w - w̅)^2)]
Using the provided values:
L = 12, 16, 16, 17, 18, 19, 21, 23
w = 8, 17, 19, 20, 27, 30, 37, 42
First, calculate the means of L and w:
L̅ = (12 + 16 + 16 + 17 + 18 + 19 + 21 + 23) / 8 = 18
w̅ = (8 + 17 + 19 + 20 + 27 + 30 + 37 + 42) / 8 = 24
Now, calculate the sums:
Σ((L - L̅)(w - w̅)) = (12 - 18)(8 - 24) + (16 - 18)(17 - 24) + (16 - 18)(19 - 24) + (17 - 18)(20 - 24) + (18 - 18)(27 - 24) + (19 - 18)(30 - 24) + (21 - 18)(37 - 24) + (23 - 18)(42 - 24) = -192
Σ(L - L̅)^2 = (12 - 18)^2 + (16 - 18)^2 + (16 - 18)^2 + (17 - 18)^2 + (18 - 18)^2 + (19 - 18)^2 + (21 - 18)^2 + (23 - 18)^2 = 52
Σ(w - w̅)^2 = (8 - 24)^2 + (17 - 24)^2 + (19 - 24)^2 + (20 - 24)^2 + (27 - 24)^2 + (30 - 24)^2 + (37 - 24)^2 + (42 - 24)^2 = 374
Substituting these values into the formula for r:
r = (-192) / (√52 * √374) ≈ -0.989
Therefore, the correlation coefficient for the given data is approximately -0.989. Option D is the correct answer.
1. To determine which linear relationship has a stronger correlation, we need to compare the absolute values of the correlation coefficients. The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, we are comparing r=−0.84 and r=0.72.
The correct answer is D. The linear relationship with r=−0.84 because the absolute value of r is closer to 1. A correlation coefficient closer to 1 (either positive or negative) indicates a stronger linear relationship than a correlation coefficient closer to 0.
To determine this, you can calculate the absolute values of both r=-0.84 and r=0.72 and compare which one is closer to 1.
2. To determine the kind of correlation between the variables (temperature and cricket chirps) with a correlation coefficient of 0.82, we need to consider the positive/negative sign and the strength of the coefficient.
The correct answer is B. a strong positive correlation. A positive correlation coefficient indicates a positive linear relationship, and a value of 0.82 suggests a strong correlation.
To determine this, you can consider the sign (positive) and magnitude (0.82) of the correlation coefficient.
3. To determine the kind of correlation between the variables (available power output and number of days since landing) with a correlation coefficient of -0.92, we need to consider the positive/negative sign and the strength of the coefficient.
The correct answer is D. a strong negative correlation. A negative correlation coefficient indicates a negative linear relationship, and a value of -0.92 suggests a strong correlation.
To determine this, you can consider the sign (negative) and magnitude (0.92) of the correlation coefficient.
4. To determine the kind of correlation between the variables (price of a house and area) with a correlation coefficient of 0.42, we need to consider the positive/negative sign and the strength of the coefficient.
The correct answer is C. a weak positive correlation. A positive correlation coefficient indicates a positive linear relationship, and a value of 0.42 suggests a weak correlation.
To determine this, you can consider the sign (positive) and magnitude (0.42) of the correlation coefficient.
5. To find the correlation coefficient for the length of fish (L) and weight of fish (w) data provided, you can use a statistical software or calculator that provides correlation analysis.
The correct answer is not provided in the options. To determine the correlation coefficient, you would typically calculate it using the formula and the given data. In this case, the only option is to perform the calculation.
Note: The correlation coefficient is a numerical value between -1 and 1, so the options B, C, and D are not valid correlation coefficient values.