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- Find the new data point (x,y) in which x=2 from the data points (1,3) and (4,12)8. Which is the linear regression equation for a scatterplot with these points rounded to the nearest tenth: (4, 35), (6.5, 92), (2. 10). (5, 50), (6, 85), (10, 110)?5. Write the equation of the least-squares regression line defining any variables used. Round coefficients to 4 decimal places .
- 75. A data set consists of the following ordered pairs: {(1, 17), (3, 13), (4, 11), (7, 5), (8, 3)} What is the equation of the linear regression model? y = -2x + 17 y = -2x + 19 y = -4x + 19 y = -4x + 17Assume we have data demonstrating a strong linear link between the amount of fertilizer applied to certain plants and their yield. Which is the independent variable in this research question?Find the least-squares regression line ŷ = ba + b₁ through the points (−2, 2), (3, 6), (5, 14), (8, 19), (10, 27), and then use it to find point estimates corresponding to x = 1 and x = = 7. For x = 1, y = For x = 7, y =
- 3. Let Q₁ be the slope and Q2 the intercept of the linear regression line y = ax + b, where the sequences x and y are as follows: x: 57, 30, 13,-57, 22, 48, -59, 74, -72, 64, -56, 21, y: -31, 45, 10, 53, 80, -22,-60, 98, -46, 57, 24, 70. - Let Q=In(3+1Q1 +2|Q2]). Then T = 5 sin² (100Q) satisfies:- (A) 0 ≤ T < 1. (B) 1≤T<2.- (C) 2≤T<3.- (D) 3 ≤ T < 4.-(E) 4≤ T ≤ 5.A researcher collected statistics on the sales amount of a product in 120 different markets and the advertising budgets used in TV, radio and newspaper media channels for each of these markets. The sales amount are expressed in 1000 units, and the budgets are expressed in 1000 $. The researcher wants to create a simple linear regression model by choosing one among the TV, radio and newspaper advertising budgets to explain the amount of sales.a) In your opinion, which variable should this researcher choose as an independent variable to the simple regression model? Explain your decision by providing its statistical basis.b) Construct the simple linear regression model using the argument you chose and write the equation of the model. Comment b0 and b1.c) Test whether there is a statistically significant, linear relationship between the independent variable and the dependent variable by establishing the relevant hypotheses at the level of α = 0.05 significance. Explain your decision and…Over a period of ten years, the number of times a certain individual has visited New York each year has been recorded. Records have also been kept of the number of incidents of major jewelry thefts in the city for each year in this period. The numbers are as follows: 17 15 22 14 9 18 10 5 Visits(xi) Thefts (yi) 6 12 5 Slope = 6 Intercept = 8 a) Determine the equation of the regression line. b) Estimate the percentage of thefts that are explained by this person's number of visits to the city each year. c) Is there a significant linear correlation between the number of visits and the number of thefts? Enter your answers below. Use 6 decimal places. 3 Use 6 decimal places. STRICTLY FOLLOW THE DECIMAL PLACES REQUIRED IN THIS PROBLEM. 7 Percentage of thefts that are explained by this person's number of visits to the city each year = Is there a significant linear correlation between the number of visits and the number of thefts (Yes or No)? - 21 5 13 5
- A linear regression to quantify the salaries of the employees in a company is estimated, using the following variables: Y: the salary of the employee in 1000 SEK. Age: the age of the employee in years R: the categorical variable Education with 3 groups; Primary, Secondary, University. a)Write down a linear model with intercept for the variable Y based on Age and R, in which the Primary level of education is the reference category for the Education variable. b)Mention a test to see if the variable Age significantly improves the model fit?In the simple linear regression model, if there is a very strong correlation between the independent and dependent variables, then the correlation coefficient should be a) close to either -1 or +1 b) close to zero c) close to -1 d) close to +1 ( don't hand writing solution)Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth. {(1, 3), (5, 12), (7, 14), (9, 19), (11, 22)} r =