3. Table 1 shows the median rent per m² in Berlin, for each of the 12 districts, and for all market segments, for the years 2020 (variable ✗) and 2021 (variable Y). For these data, the following is known: 12 IM i=1 (b) 12 12 12 12 for π; = 124.31, Σy = 127.93, Στ = 1326.6657, Σy = 1408.3461, Σriyi = 1365.7266 i=1 Calculate and y. 2=1 i=1 i=1 Calculate the sample variance for X and Y. Hint: For the sample variance the following formula holds: (c) (d) n Σ? - 2 Σ + n n 1 S = n-1 i=1 i=1 Calculate the sample standard deviation for X and Y. Calculate the covariance and the correlation coefficient. Recall: The formula for the correlation coefficient is suitable SXY TXY = SXSY

Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m = 8, x = 114.6, s1 = 5.03, n = 8, y = 129.3, and s2 = 5.38. Calculate a 95% CI for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2. (Round your answers to two decimal places.)      ,

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.9 8.1 6.9 3.8 2.3 2.7 2.4 0.7 yy 13.9 11.2 9.7 7.2 5.8 6.4 5.9 4.9 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.83x+4.08.y=0.83x+4.08. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 9 thousand automatic weapons?Answer =  Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 4 thousand automatic weapons?Answer =  Round to 3 decimal places.

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.4 7 3.8 2.7 2.3 2.5 0.3 yy 14.2 11.4 10.2 7.4 6.3 6.1 6 4 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation ˆy=0.89x+3.89.y^=0.89x+3.89. Use this equation to answer the following;Note: Verify this equation using your calculator.A) How many murders per 100,000 residents can be expected in a state with 2.8 thousand automatic weapons?Answer =  Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 8.5 thousand automatic weapons?Answer =  Round to 3 decimal places.

If the coefficient of determination (R2) value is 0.99, it means the 99% of ____________ of the observed y-values of are explained by the __________ of the predicted y-values, and only 1% remains unexplained.

Assume that monthly income follows a normal distribution with population mean µ = $4,000 and population standard deviation σ = $1000.A government agency wants to provide free health care to all individuals earning below a specified monthly income but the agency does not want to award this benefit to more than 1.1 percent (or 0.0110) of the population. What should this income cutoff be to make sure that not more than 5 percent of the population receive this free health care benefit? Show your work by providing the relevant equations and the final answer.

1. Referring to Scenario 13-11, which of the following is the correct interpretation for the slope coefficient?a) For each decrease of 1 thousand downloads, the expected revenue is estimated to increase by $ 3.7297 thousands.b) For each increase of 1 thousand downloads, the expected revenue is estimated to increase by $ 3.7297 thousands.c) For each decrease of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands.d) For each increase of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands.

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.9 8.3 6.9 3.9 2.7 2.4 2.1 0.7 yy 14.3 11.3 10 7.4 6.5 6.4 5.9 4.9 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.84x+4.23. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.Use the equation with the values rounded to two decimal places to make your predictions.A) How many murders per 100,000 residents can be expected in a state with 5.5 thousand automatic weapons?Answer =  Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 3.9 thousand automatic weapons?Answer =  Round to 3 decimal places.

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.3 8.6 7.1 3.3 2.4 2.3 2.4 0.7 yy 13.7 11.1 10.4 6.9 6.4 6.2 6.1 4.9 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.83x+4.28.y=0.83x+4.28. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 10.7 thousand automatic weapons?Answer =  Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 1.6 thousand automatic weapons?Answer =  Round to 3 decimal places.The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.3 8.6 7.1 3.3 2.4 2.3 2.4 0.7 yy 13.7 11.1 10.4 6.9 6.4 6.2 6.1 4.9 xx = thousands of…

The relationship between sleep hours and overall happiness level on the next day was estimated as below in a linear format. (Happiness level is measured through a five-point scale: 1 = Extremely unhappy, 5 = Extremely happy)   Overall happiness level = 0.27 * Sleep hours + 2.34 (The p-value for the coefficient of Sleep hours is 0.02.)   Based on this equation, what is the expected happiness level of a person on a certain day, when he slept 7 hours the day before?